# spacegroups

hm_notation: C 1 2/c 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: R -3 c
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,1/2+z", "2/3+x,1/3+x-y,5/6+z", "1/3+x,2/3+x-y,1/6+z", "y,x,1/2-z", "2/3+y,1/3+x,5/6-z", "1/3+y,2/3+x,1/6-z", "-x+y,y,1/2+z", "2/3-x+y,1/3+y,5/6+z", "1/3-x+y,2/3+y,1/6+z", "-x,-x+y,1/2-z", "2/3-x,1/3-x+y,5/6-z", "1/3-x,2/3-x+y,1/6-z", "-y,-x,1/2+z", "2/3-y,1/3-x,5/6+z", "1/3-y,2/3-x,1/6+z", "x-y,-y,1/2-z", "2/3+x-y,1/3-y,5/6-z", "1/3+x-y,2/3-y,1/6-z", "y,-x+y,-z", "2/3+y,1/3-x+y,1/3-z", "1/3+y,2/3-x+y,2/3-z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z", "-x,-y,-z", "2/3-x,1/3-y,1/3-z", "1/3-x,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "x-y,x,-z", "2/3+x-y,1/3+x,1/3-z", "1/3+x-y,2/3+x,2/3-z"]


hm_notation: F d -3 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,1/2-x,1/4+y", "3/4+z,-x,3/4+y", "1/4+z,1/2-x,3/4+y", "1/4+z,-x,1/4+y", "3/4-y,1/2+z,1/4-x", "3/4-y,+z,3/4-x", "1/4-y,1/2+z,3/4-x", "1/4-y,+z,1/4-x", "3/4+x,1/2-y,1/4+z", "3/4+x,-y,3/4+z", "1/4+x,1/2-y,3/4+z", "1/4+x,-y,1/4+z", "3/4-z,1/2+x,1/4-y", "3/4-z,+x,3/4-y", "1/4-z,1/2+x,3/4-y", "1/4-z,+x,1/4-y", "3/4+y,1/2-z,1/4+x", "3/4+y,-z,3/4+x", "1/4+y,1/2-z,3/4+x", "1/4+y,-z,1/4+x", "3/4-x,1/2+y,1/4-z", "3/4-x,+y,3/4-z", "1/4-x,1/2+y,3/4-z", "1/4-x,+y,1/4-z", "1/2+x,3/4-z,1/4-y", "1/2+x,1/4-z,3/4-y", "+x,3/4-z,3/4-y", "+x,1/4-z,1/4-y", "1/2-z,3/4+y,1/4+x", "1/2-z,1/4+y,3/4+x", "-z,3/4+y,3/4+x", "-z,1/4+y,1/4+x", "1/2+y,3/4-x,1/4-z", "1/2+y,1/4-x,3/4-z", "+y,3/4-x,3/4-z", "+y,1/4-x,1/4-z", "1/2-x,3/4+z,1/4+y", "1/2-x,1/4+z,3/4+y", "-x,3/4+z,3/4+y", "-x,1/4+z,1/4+y", "1/2+z,3/4-y,1/4-x", "1/2+z,1/4-y,3/4-x", "+z,3/4-y,3/4-x", "+z,1/4-y,1/4-x", "1/2-y,3/4+x,1/4+z", "1/2-y,1/4+x,3/4+z", "-y,3/4+x,3/4+z", "-y,1/4+x,1/4+z", "x,1/2+z,1/2+y", "x,+z,+y", "1/2+x,1/2+z,+y", "1/2+x,+z,1/2+y", "-z,1/2-y,1/2-x", "-z,-y,-x", "1/2-z,1/2-y,-x", "1/2-z,-y,1/2-x", "y,1/2+x,1/2+z", "y,+x,+z", "1/2+y,1/2+x,+z", "1/2+y,+x,1/2+z", "-x,1/2-z,1/2-y", "-x,-z,-y", "1/2-x,1/2-z,-y", "1/2-x,-z,1/2-y", "z,1/2+y,1/2+x", "z,+y,+x", "1/2+z,1/2+y,+x", "1/2+z,+y,1/2+x", "-y,1/2-x,1/2-z", "-y,-x,-z", "1/2-y,1/2-x,-z", "1/2-y,-x,1/2-z", "3/4+z,1/4+x,1/2-y", "3/4+z,3/4+x,-y", "1/4+z,1/4+x,-y", "1/4+z,3/4+x,1/2-y", "3/4-y,1/4-z,1/2+x", "3/4-y,3/4-z,+x", "1/4-y,1/4-z,+x", "1/4-y,3/4-z,1/2+x", "3/4+x,1/4+y,1/2-z", "3/4+x,3/4+y,-z", "1/4+x,1/4+y,-z", "1/4+x,3/4+y,1/2-z", "3/4-z,1/4-x,1/2+y", "3/4-z,3/4-x,+y", "1/4-z,1/4-x,+y", "1/4-z,3/4-x,1/2+y", "3/4+y,1/4+z,1/2-x", "3/4+y,3/4+z,-x", "1/4+y,1/4+z,-x", "1/4+y,3/4+z,1/2-x", "3/4-x,1/4-y,1/2+z", "3/4-x,3/4-y,+z", "1/4-x,1/4-y,+z", "1/4-x,3/4-y,1/2+z", "-z,3/4+x,3/4+y", "-z,1/4+x,1/4+y", "1/2-z,3/4+x,1/4+y", "1/2-z,1/4+x,3/4+y", "y,3/4-z,3/4-x", "y,1/4-z,1/4-x", "1/2+y,3/4-z,1/4-x", "1/2+y,1/4-z,3/4-x", "-x,3/4+y,3/4+z", "-x,1/4+y,1/4+z", "1/2-x,3/4+y,1/4+z", "1/2-x,1/4+y,3/4+z", "z,3/4-x,3/4-y", "z,1/4-x,1/4-y", "1/2+z,3/4-x,1/4-y", "1/2+z,1/4-x,3/4-y", "-y,3/4+z,3/4+x", "-y,1/4+z,1/4+x", "1/2-y,3/4+z,1/4+x", "1/2-y,1/4+z,3/4+x", "x,3/4-y,3/4-z", "x,1/4-y,1/4-z", "1/2+x,3/4-y,1/4-z", "1/2+x,1/4-y,3/4-z", "1/4-x,1/2+z,3/4-y", "1/4-x,+z,1/4-y", "3/4-x,1/2+z,1/4-y", "3/4-x,+z,3/4-y", "1/4+z,1/2-y,3/4+x", "1/4+z,-y,1/4+x", "3/4+z,1/2-y,1/4+x", "3/4+z,-y,3/4+x", "1/4-y,1/2+x,3/4-z", "1/4-y,+x,1/4-z", "3/4-y,1/2+x,1/4-z", "3/4-y,+x,3/4-z", "1/4+x,1/2-z,3/4+y", "1/4+x,-z,1/4+y", "3/4+x,1/2-z,1/4+y", "3/4+x,-z,3/4+y", "1/4-z,1/2+y,3/4-x", "1/4-z,+y,1/4-x", "3/4-z,1/2+y,1/4-x", "3/4-z,+y,3/4-x", "1/4+y,1/2-x,3/4+z", "1/4+y,-x,1/4+z", "3/4+y,1/2-x,1/4+z", "3/4+y,-x,3/4+z", "3/4-x,3/4-z,y", "3/4-x,1/4-z,1/2+y", "1/4-x,3/4-z,1/2+y", "1/4-x,1/4-z,y", "3/4+z,3/4+y,-x", "3/4+z,1/4+y,1/2-x", "1/4+z,3/4+y,1/2-x", "1/4+z,1/4+y,-x", "3/4-y,3/4-x,z", "3/4-y,1/4-x,1/2+z", "1/4-y,3/4-x,1/2+z", "1/4-y,1/4-x,z", "3/4+x,3/4+z,-y", "3/4+x,1/4+z,1/2-y", "1/4+x,3/4+z,1/2-y", "1/4+x,1/4+z,-y", "3/4-z,3/4-y,x", "3/4-z,1/4-y,1/2+x", "1/4-z,3/4-y,1/2+x", "1/4-z,1/4-y,x", "3/4+y,3/4+x,-z", "3/4+y,1/4+x,1/2-z", "1/4+y,3/4+x,1/2-z", "1/4+y,1/4+x,-z", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x"]


hm_notation: P n n a
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,y,-z", "1/2-x,-y,z", "-x,-y,-z"]


hm_notation: P -4 3 m
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "x,-z,-y", "z,-y,-x", "y,-x,-z", "x,z,y", "z,y,x", "y,x,z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "-x,z,-y", "-z,y,-x", "-y,x,-z", "-x,-z,y", "-z,-y,x", "-y,-x,z", "z,x,y", "y,z,x"]


hm_notation: P -6 2 m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "-x+y,-x,-z", "y,x,-z", "-y,x-y,z", "x-y,-y,z", "x,y,-z", "-x,-x+y,-z", "-x+y,-x,z", "y,x,z", "-y,x-y,-z", "x-y,-y,-z"]


hm_notation: P 4/m m m
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "y,-x,-z", "-y,x,z", "x,-y,z", "-x,y,-z", "x,y,-z", "-x,-y,z", "y,x,z", "-y,-x,-z", "-y,x,-z", "y,-x,z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: C 1 2/m 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P n m a
symmetry_xyz:
["x,y,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: P -4 3 n
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "1/2+x,1/2-z,1/2-y", "1/2+z,1/2-y,1/2-x", "1/2+y,1/2-x,1/2-z", "1/2+x,1/2+z,1/2+y", "1/2+z,1/2+y,1/2+x", "1/2+y,1/2+x,1/2+z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "1/2-x,1/2+z,1/2-y", "1/2-z,1/2+y,1/2-x", "1/2-y,1/2+x,1/2-z", "1/2-x,1/2-z,1/2+y", "1/2-z,1/2-y,1/2+x", "1/2-y,1/2-x,1/2+z", "z,x,y", "y,z,x"]


hm_notation: P b c m
symmetry_xyz:
["x,y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,1/2+y,z", "x,1/2-y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: P n a m
symmetry_xyz:
["x,y,z", "x,y,1/2-z", "-x,-y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: I -4 3 d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-z,x,-y", "-z,1/2+x,1/2-y", "1/2-y,z,-x", "-y,1/2+z,1/2-x", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/4+x,3/4-z,1/4-y", "3/4+x,1/4-z,3/4-y", "1/4+z,3/4-y,1/4-x", "3/4+z,1/4-y,3/4-x", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4+x,1/4+z,1/4+y", "3/4+x,3/4+z,3/4+y", "1/4+z,1/4+y,1/4+x", "3/4+z,3/4+y,3/4+x", "1/4+y,1/4+x,1/4+z", "3/4+y,3/4+x,3/4+z", "-z,1/2-x,y", "1/2-z,-x,1/2+y", "-y,1/2-z,x", "1/2-y,-z,1/2+x", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "3/4-x,3/4+z,1/4-y", "1/4-x,1/4+z,3/4-y", "3/4-z,3/4+y,1/4-x", "1/4-z,1/4+y,3/4-x", "3/4-y,3/4+x,1/4-z", "1/4-y,1/4+x,3/4-z", "3/4-x,1/4-z,1/4+y", "1/4-x,3/4-z,3/4+y", "3/4-z,1/4-y,1/4+x", "1/4-z,3/4-y,3/4+x", "3/4-y,1/4-x,1/4+z", "1/4-y,3/4-x,3/4+z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: I -4
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z"]


hm_notation: R -3 m
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,z", "2/3+x,1/3+x-y,1/3+z", "1/3+x,2/3+x-y,2/3+z", "y,x,-z", "2/3+y,1/3+x,1/3-z", "1/3+y,2/3+x,2/3-z", "-x+y,y,z", "2/3-x+y,1/3+y,1/3+z", "1/3-x+y,2/3+y,2/3+z", "-x,-x+y,-z", "2/3-x,1/3-x+y,1/3-z", "1/3-x,2/3-x+y,2/3-z", "-y,-x,z", "2/3-y,1/3-x,1/3+z", "1/3-y,2/3-x,2/3+z", "x-y,-y,-z", "2/3+x-y,1/3-y,1/3-z", "1/3+x-y,2/3-y,2/3-z", "y,-x+y,-z", "2/3+y,1/3-x+y,1/3-z", "1/3+y,2/3-x+y,2/3-z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z", "-x,-y,-z", "2/3-x,1/3-y,1/3-z", "1/3-x,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "x-y,x,-z", "2/3+x-y,1/3+x,1/3-z", "1/3+x-y,2/3+x,2/3-z"]


hm_notation: P -3 1 c
symmetry_xyz:
["x,y,z", "x-y,-y,1/2+z", "y,-x+y,-z", "-y,-x,1/2-z", "-x+y,-x,z", "-x,-x+y,1/2+z", "-x,-y,-z", "-x+y,y,1/2-z", "-y,x-y,z", "y,x,1/2+z", "x-y,x,-z", "x,x-y,1/2-z"]


hm_notation: P 63 m c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "x-y,x,1/2+z", "-y,-x,z", "-y,x-y,z", "x-y,-y,1/2+z", "-x,-y,1/2+z", "x,x-y,z", "-x+y,-x,z", "y,x,1/2+z", "y,-x+y,1/2+z", "-x+y,y,z"]


hm_notation: A m a m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P n m n
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "x,-y,z", "-x,y,-z", "-x,-y,-z"]


hm_notation: F m 3 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "z,-x,y", "z,1/2-x,1/2+y", "1/2+z,-x,1/2+y", "1/2+z,1/2-x,y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "y,-z,x", "y,1/2-z,1/2+x", "1/2+y,-z,1/2+x", "1/2+y,1/2-z,x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,-y", "x,1/2-z,1/2-y", "1/2+x,-z,1/2-y", "1/2+x,1/2-z,-y", "-z,y,x", "-z,1/2+y,1/2+x", "1/2-z,y,1/2+x", "1/2-z,1/2+y,x", "y,-x,-z", "y,1/2-x,1/2-z", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "-x,z,y", "-x,1/2+z,1/2+y", "1/2-x,z,1/2+y", "1/2-x,1/2+z,y", "z,-y,-x", "z,1/2-y,1/2-x", "1/2+z,-y,1/2-x", "1/2+z,1/2-y,-x", "-y,x,z", "-y,1/2+x,1/2+z", "1/2-y,x,1/2+z", "1/2-y,1/2+x,z", "x,z,y", "x,1/2+z,1/2+y", "1/2+x,z,1/2+y", "1/2+x,1/2+z,y", "-z,-y,-x", "-z,1/2-y,1/2-x", "1/2-z,-y,1/2-x", "1/2-z,1/2-y,-x", "y,x,z", "y,1/2+x,1/2+z", "1/2+y,x,1/2+z", "1/2+y,1/2+x,z", "-x,-z,-y", "-x,1/2-z,1/2-y", "1/2-x,-z,1/2-y", "1/2-x,1/2-z,-y", "z,y,x", "z,1/2+y,1/2+x", "1/2+z,y,1/2+x", "1/2+z,1/2+y,x", "-y,-x,-z", "-y,1/2-x,1/2-z", "1/2-y,-x,1/2-z", "1/2-y,1/2-x,-z", "z,x,-y", "z,1/2+x,1/2-y", "1/2+z,x,1/2-y", "1/2+z,1/2+x,-y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "y,z,-x", "y,1/2+z,1/2-x", "1/2+y,z,1/2-x", "1/2+y,1/2+z,-x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "-z,x,y", "-z,1/2+x,1/2+y", "1/2-z,x,1/2+y", "1/2-z,1/2+x,y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "-y,z,x", "-y,1/2+z,1/2+x", "1/2-y,z,1/2+x", "1/2-y,1/2+z,x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,-y", "-x,1/2+z,1/2-y", "1/2-x,z,1/2-y", "1/2-x,1/2+z,-y", "z,-y,x", "z,1/2-y,1/2+x", "1/2+z,-y,1/2+x", "1/2+z,1/2-y,x", "-y,x,-z", "-y,1/2+x,1/2-z", "1/2-y,x,1/2-z", "1/2-y,1/2+x,-z", "x,-z,y", "x,1/2-z,1/2+y", "1/2+x,-z,1/2+y", "1/2+x,1/2-z,y", "-z,y,-x", "-z,1/2+y,1/2-x", "1/2-z,y,1/2-x", "1/2-z,1/2+y,-x", "y,-x,z", "y,1/2-x,1/2+z", "1/2+y,-x,1/2+z", "1/2+y,1/2-x,z", "-x,-z,y", "-x,1/2-z,1/2+y", "1/2-x,-z,1/2+y", "1/2-x,1/2-z,y", "z,y,-x", "z,1/2+y,1/2-x", "1/2+z,y,1/2-x", "1/2+z,1/2+y,-x", "-y,-x,z", "-y,1/2-x,1/2+z", "1/2-y,-x,1/2+z", "1/2-y,1/2-x,z", "x,z,-y", "x,1/2+z,1/2-y", "1/2+x,z,1/2-y", "1/2+x,1/2+z,-y", "-z,-y,x", "-z,1/2-y,1/2+x", "1/2-z,-y,1/2+x", "1/2-z,1/2-y,x", "y,x,-z", "y,1/2+x,1/2-z", "1/2+y,x,1/2-z", "1/2+y,1/2+x,-z", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x"]


hm_notation: C 2 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "x,-y,-z", "1/2+x,1/2-y,-z", "-x,-y,z", "1/2-x,1/2-y,z"]


hm_notation: F d d d
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4-x,y,3/4-z", "3/4-x,1/2+y,1/4-z", "1/4-x,y,1/4-z", "1/4-x,1/2+y,3/4-z", "-x,3/4+y,3/4+z", "-x,1/4+y,1/4+z", "1/2-x,3/4+y,1/4+z", "1/2-x,1/4+y,3/4+z", "x,3/4-y,3/4-z", "x,1/4-y,1/4-z", "1/2+x,3/4-y,1/4-z", "1/2+x,1/4-y,3/4-z", "3/4+x,3/4+y,-z", "3/4+x,1/4+y,1/2-z", "1/4+x,3/4+y,1/2-z", "1/4+x,1/4+y,-z", "3/4-x,3/4-y,z", "3/4-x,1/4-y,1/2+z", "1/4-x,3/4-y,1/2+z", "1/4-x,1/4-y,z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: R 3 2
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "-x,-x+y,-z", "2/3-x,1/3-x+y,1/3-z", "1/3-x,2/3-x+y,2/3-z", "y,x,-z", "2/3+y,1/3+x,1/3-z", "1/3+y,2/3+x,2/3-z", "x-y,-y,-z", "2/3+x-y,1/3-y,1/3-z", "1/3+x-y,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: P c a m
symmetry_xyz:
["x,y,z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,-y,z", "1/2-x,y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: P b n m
symmetry_xyz:
["x,y,z", "x,y,1/2-z", "-x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P -4 21 c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,-x,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,x,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P 41 21 2
symmetry_xyz:
["x,y,z", "y,x,-z", "1/2-y,1/2+x,1/4+z", "1/2-x,1/2+y,1/4-z", "-x,-y,1/2+z", "-y,-x,1/2-z", "1/2+y,1/2-x,3/4+z", "1/2+x,1/2-y,3/4-z"]


hm_notation: P m n n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: I m m a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "-x,1/2+y,-z", "1/2-x,+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: C m c 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z"]


hm_notation: R -3 %var1%
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "y,-x+y,-z", "2/3+y,1/3-x+y,1/3-z", "1/3+y,2/3-x+y,2/3-z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z", "-x,-y,-z", "2/3-x,1/3-y,1/3-z", "1/3-x,2/3-y,2/3-z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "x-y,x,-z", "2/3+x-y,1/3+x,1/3-z", "1/3+x-y,2/3+x,2/3-z"]


hm_notation: P a 3
symmetry_xyz:
["x,y,z", "1/2+z,x,1/2-y", "z,1/2-x,1/2+y", "1/2-z,1/2+x,y", "-z,-x,-y", "1/2+y,1/2-z,-x", "1/2-y,-z,1/2+x", "-y,1/2+z,1/2-x", "y,z,x", "x,1/2-y,1/2+z", "1/2-x,1/2+y,z", "1/2+x,y,1/2-z", "-x,-y,-z", "1/2-z,-x,1/2+y", "-z,1/2+x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "1/2-y,1/2+z,x", "1/2+y,z,1/2-x", "y,1/2-z,1/2+x", "-y,-z,-x", "-x,1/2+y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,-y,1/2+z"]


hm_notation: P b c n
symmetry_xyz:
["x,y,z", "x,-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: I 4/m m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "y,x,-z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,z", "1/2+y,1/2+x,1/2+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 6/m c c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "x,x-y,1/2-z", "-x+y,-x,-z", "x-y,x,z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,1/2+z", "-x+y,y,1/2-z", "x,y,-z", "-x,-y,z", "x,x-y,1/2+z", "-x,-x+y,1/2-z", "x-y,x,-z", "-x+y,-x,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x-y,-z", "y,-x+y,z", "-x+y,y,1/2+z", "x-y,-y,1/2-z", "-x,-y,-z"]


hm_notation: P -3 m 1
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,-x+y,-z", "-x,-x+y,-z", "-x+y,-x,z", "-x+y,y,z", "-x,-y,-z", "y,x,-z", "-y,x-y,z", "x,x-y,z", "x-y,x,-z", "x-y,-y,-z"]


hm_notation: I 1 2/m 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: F -4 3 c
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,1/2-y", "x,1/2-z,-y", "1/2+x,-z,-y", "1/2+x,1/2-z,1/2-y", "z,-y,1/2-x", "z,1/2-y,-x", "1/2+z,-y,-x", "1/2+z,1/2-y,1/2-x", "y,-x,1/2-z", "y,1/2-x,-z", "1/2+y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,z,1/2+y", "x,1/2+z,+y", "1/2+x,z,+y", "1/2+x,1/2+z,1/2+y", "z,y,1/2+x", "z,1/2+y,+x", "1/2+z,y,+x", "1/2+z,1/2+y,1/2+x", "y,x,1/2+z", "y,1/2+x,+z", "1/2+y,x,+z", "1/2+y,1/2+x,1/2+z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,1/2-y", "-x,1/2+z,-y", "1/2-x,z,-y", "1/2-x,1/2+z,1/2-y", "-z,y,1/2-x", "-z,1/2+y,-x", "1/2-z,y,-x", "1/2-z,1/2+y,1/2-x", "-y,x,1/2-z", "-y,1/2+x,-z", "1/2-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,-z,1/2+y", "-x,1/2-z,+y", "1/2-x,-z,+y", "1/2-x,1/2-z,1/2+y", "-z,-y,1/2+x", "-z,1/2-y,+x", "1/2-z,-y,+x", "1/2-z,1/2-y,1/2+x", "-y,-x,1/2+z", "-y,1/2-x,+z", "1/2-y,-x,+z", "1/2-y,1/2-x,1/2+z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x"]


hm_notation: P c c n
symmetry_xyz:
["x,y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,-y,-z"]


hm_notation: P m 3 m
symmetry_xyz:
["x,y,z", "z,-x,y", "-y,z,-x", "x,-y,z", "-z,x,-y", "y,-z,x", "-x,y,-z", "x,-z,-y", "-z,y,x", "y,-x,-z", "-x,z,y", "z,-y,-x", "-y,x,z", "x,z,y", "-z,-y,-x", "y,x,z", "-x,-z,-y", "z,y,x", "-y,-x,-z", "z,x,-y", "-y,-z,x", "x,y,-z", "-z,-x,y", "y,z,-x", "-x,-y,z", "-z,x,y", "y,-z,-x", "-x,y,z", "z,-x,-y", "-y,z,x", "x,-y,-z", "-x,z,-y", "z,-y,x", "-y,x,-z", "x,-z,y", "-z,y,-x", "y,-x,z", "-x,-z,y", "z,y,-x", "-y,-x,z", "x,z,-y", "-z,-y,x", "y,x,-z", "-z,-x,-y", "y,z,x", "-x,-y,-z", "z,x,y", "-y,-z,-x"]


hm_notation: P c m n
symmetry_xyz:
["x,y,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 63/m m c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "x,x-y,1/2-z", "-x+y,-x,1/2-z", "x-y,x,1/2+z", "-y,-x,z", "y,x,-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,1/2+z", "-x+y,y,1/2-z", "x,y,1/2-z", "-x,-y,1/2+z", "x,x-y,z", "-x,-x+y,-z", "x-y,x,-z", "-x+y,-x,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x-y,1/2-z", "y,-x+y,1/2+z", "-x+y,y,z", "x-y,-y,-z", "-x,-y,-z"]


hm_notation: I 1 2/c 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 41/a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "3/4+y,1/4-x,1/4-z", "1/4+y,3/4-x,3/4-z", "3/4-y,1/4+x,1/4+z", "1/4-y,3/4+x,3/4+z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "3/4-y,3/4+x,3/4-z", "1/4-y,1/4+x,1/4-z", "3/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 4/m c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,1/2+z", "1/2-y,1/2-x,+z", "y,x,1/2-z", "1/2+y,1/2+x,-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,1/2+z", "1/2+y,1/2+x,+z", "-y,-x,1/2-z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: A c a m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,1/2+y,z", "1/2-x,+y,1/2+z", "1/2+x,1/2-y,-z", "1/2+x,-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I 41/a m d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/4-y,3/4-x,1/4+z", "3/4-y,1/4-x,3/4+z", "1/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/2+x,-y,1/2+z", "+x,1/2-y,+z", "1/2-x,y,1/2-z", "-x,1/2+y,-z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/4+y,1/4+x,3/4+z", "3/4+y,3/4+x,1/4+z", "1/4-y,1/4-x,3/4-z", "3/4-y,3/4-x,1/4-z", "1/4-y,1/4+x,3/4-z", "3/4-y,3/4+x,1/4-z", "1/4+y,1/4-x,3/4+z", "3/4+y,3/4-x,1/4+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P n c n
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "x,-y,1/2+z", "-x,y,1/2-z", "-x,-y,-z"]


hm_notation: C m c a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,1/2+y,1/2-z", "1/2+x,+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: C c c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,1/2-z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F m 3 c
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "z,-x,y", "z,1/2-x,1/2+y", "1/2+z,-x,1/2+y", "1/2+z,1/2-x,y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "y,-z,x", "y,1/2-z,1/2+x", "1/2+y,-z,1/2+x", "1/2+y,1/2-z,x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,1/2-y", "x,1/2-z,-y", "1/2+x,-z,-y", "1/2+x,1/2-z,1/2-y", "-z,y,1/2+x", "-z,1/2+y,+x", "1/2-z,y,+x", "1/2-z,1/2+y,1/2+x", "y,-x,1/2-z", "y,1/2-x,-z", "1/2+y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,z,1/2+y", "-x,1/2+z,+y", "1/2-x,z,+y", "1/2-x,1/2+z,1/2+y", "z,-y,1/2-x", "z,1/2-y,-x", "1/2+z,-y,-x", "1/2+z,1/2-y,1/2-x", "-y,x,1/2+z", "-y,1/2+x,+z", "1/2-y,x,+z", "1/2-y,1/2+x,1/2+z", "x,z,1/2+y", "x,1/2+z,+y", "1/2+x,z,+y", "1/2+x,1/2+z,1/2+y", "-z,-y,1/2-x", "-z,1/2-y,-x", "1/2-z,-y,-x", "1/2-z,1/2-y,1/2-x", "y,x,1/2+z", "y,1/2+x,+z", "1/2+y,x,+z", "1/2+y,1/2+x,1/2+z", "-x,-z,1/2-y", "-x,1/2-z,-y", "1/2-x,-z,-y", "1/2-x,1/2-z,1/2-y", "z,y,1/2+x", "z,1/2+y,+x", "1/2+z,y,+x", "1/2+z,1/2+y,1/2+x", "-y,-x,1/2-z", "-y,1/2-x,-z", "1/2-y,-x,-z", "1/2-y,1/2-x,1/2-z", "z,x,-y", "z,1/2+x,1/2-y", "1/2+z,x,1/2-y", "1/2+z,1/2+x,-y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "y,z,-x", "y,1/2+z,1/2-x", "1/2+y,z,1/2-x", "1/2+y,1/2+z,-x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "-z,x,y", "-z,1/2+x,1/2+y", "1/2-z,x,1/2+y", "1/2-z,1/2+x,y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "-y,z,x", "-y,1/2+z,1/2+x", "1/2-y,z,1/2+x", "1/2-y,1/2+z,x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,1/2-y", "-x,1/2+z,-y", "1/2-x,z,-y", "1/2-x,1/2+z,1/2-y", "z,-y,1/2+x", "z,1/2-y,+x", "1/2+z,-y,+x", "1/2+z,1/2-y,1/2+x", "-y,x,1/2-z", "-y,1/2+x,-z", "1/2-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,-z,1/2+y", "x,1/2-z,+y", "1/2+x,-z,+y", "1/2+x,1/2-z,1/2+y", "-z,y,1/2-x", "-z,1/2+y,-x", "1/2-z,y,-x", "1/2-z,1/2+y,1/2-x", "y,-x,1/2+z", "y,1/2-x,+z", "1/2+y,-x,+z", "1/2+y,1/2-x,1/2+z", "-x,-z,1/2+y", "-x,1/2-z,+y", "1/2-x,-z,+y", "1/2-x,1/2-z,1/2+y", "z,y,1/2-x", "z,1/2+y,-x", "1/2+z,y,-x", "1/2+z,1/2+y,1/2-x", "-y,-x,1/2+z", "-y,1/2-x,+z", "1/2-y,-x,+z", "1/2-y,1/2-x,1/2+z", "x,z,1/2-y", "x,1/2+z,-y", "1/2+x,z,-y", "1/2+x,1/2+z,1/2-y", "-z,-y,1/2+x", "-z,1/2-y,+x", "1/2-z,-y,+x", "1/2-z,1/2-y,1/2+x", "y,x,1/2-z", "y,1/2+x,-z", "1/2+y,x,-z", "1/2+y,1/2+x,1/2-z", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x"]


hm_notation: C m c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,y,1/2-z", "1/2+x,1/2+y,1/2-z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P 4/n m m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,x,-z", "y,-x,-z", "1/2-y,1/2+x,z", "x,-y,z", "1/2-x,1/2+y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,-x,-z", "-y,x,-z", "1/2+y,1/2-x,z", "-x,y,z", "1/2+x,1/2-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: C c c a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,-z", "-x,1/2+y,1/2+z", "1/2-x,+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,1/2+y,1/2-z", "1/2+x,+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z"]


hm_notation: P c c a
symmetry_xyz:
["x,y,z", "x,-y,1/2+z", "-x,y,1/2-z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,y,-z", "1/2-x,-y,z", "-x,-y,-z"]


hm_notation: P 63/m
symmetry_xyz:
["x,y,z", "-x+y,-x,1/2-z", "x-y,x,1/2+z", "y,-x+y,-z", "-y,x-y,z", "x,y,1/2-z", "-x,-y,1/2+z", "x-y,x,-z", "-x+y,-x,z", "-y,x-y,1/2-z", "y,-x+y,1/2+z", "-x,-y,-z"]


hm_notation: B 2 m b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z"]


hm_notation: I 41/a %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/4-y,1/4+x,3/4-z", "3/4-y,3/4+x,1/4-z", "1/4+y,1/4-x,3/4+z", "3/4+y,3/4-x,1/4+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P m c n
symmetry_xyz:
["x,y,z", "1/2-x,y,z", "1/2+x,-y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: P b c a
symmetry_xyz:
["x,y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: I 4/m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 1 2/a 1
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 63/m c m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "x,x-y,-z", "-x+y,-x,1/2-z", "x-y,x,1/2+z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,z", "-x+y,y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "x,x-y,1/2+z", "-x,-x+y,1/2-z", "x-y,x,-z", "-x+y,-x,z", "y,x,z", "-y,-x,-z", "-y,x-y,1/2-z", "y,-x+y,1/2+z", "-x+y,y,1/2+z", "x-y,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 21 3
symmetry_xyz:
["x,y,z", "1/2-z,-x,1/2+y", "-z,1/2+x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "1/2+y,1/2-z,-x", "1/2-y,-z,1/2+x", "-y,1/2+z,1/2-x", "y,z,x", "-x,1/2+y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,-y,1/2+z"]


hm_notation: P 4 b m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "-y,x,z", "1/2+x,1/2-y,z", "-x,-y,z", "1/2+y,1/2+x,z", "y,-x,z", "1/2-x,1/2+y,z"]


hm_notation: R 3 c
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,1/2+z", "2/3+x,1/3+x-y,5/6+z", "1/3+x,2/3+x-y,1/6+z", "-y,-x,1/2+z", "2/3-y,1/3-x,5/6+z", "1/3-y,2/3-x,1/6+z", "-x+y,y,1/2+z", "2/3-x+y,1/3+y,5/6+z", "1/3-x+y,2/3+y,1/6+z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: I 41/a c d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,1/2-x,3/4+z", "1/2-y,-x,1/4+z", "1/2+y,1/2+x,-z", "+y,+x,1/2-z", "1/2+y,1/2-x,1/2-z", "+y,-x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "1/2-x,y,1/4-z", "-x,1/2+y,3/4-z", "1/2+x,y,3/4-z", "+x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "1/2+y,x,1/4+z", "+y,1/2+x,3/4+z", "-y,-x,1/2-z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,1/2-y,3/4-z", "1/2+x,-y,1/4-z", "-x,1/2-y,1/4-z", "1/2-x,-y,3/4-z"]


hm_notation: I a 3 d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "z,1/2-x,1/2+y", "1/2+z,-x,+y", "-y,1/2+z,1/2-x", "1/2-y,+z,-x", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-z,1/2+x,1/2-y", "1/2-z,+x,-y", "y,1/2-z,1/2+x", "1/2+y,-z,+x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "3/4+x,1/4-z,3/4-y", "1/4+x,3/4-z,1/4-y", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,1/4+x", "3/4+y,1/4-x,3/4-z", "1/4+y,3/4-x,1/4-z", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,1/4+y", "3/4+z,1/4-y,3/4-x", "1/4+z,3/4-y,1/4-x", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,1/4+z", "1/4+x,1/4+z,1/4+y", "3/4+x,3/4+z,3/4+y", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,3/4-x", "1/4+y,1/4+x,1/4+z", "3/4+y,3/4+x,3/4+z", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,3/4-y", "1/4+z,1/4+y,1/4+x", "3/4+z,3/4+y,3/4+x", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/2+z,x,1/2-y", "+z,1/2+x,-y", "1/2-y,-z,1/2+x", "-y,1/2-z,+x", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "1/2+y,z,1/2-x", "+y,1/2+z,-x", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/2-z,1/2+x,y", "-z,+x,1/2+y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2-x,1/2+y,z", "-x,+y,1/2+z", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "1/2-y,1/2+z,x", "-y,+z,1/2+x", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "3/4-x,3/4+z,1/4-y", "1/4-x,1/4+z,3/4-y", "3/4+z,3/4-y,1/4+x", "1/4+z,1/4-y,3/4+x", "3/4-y,3/4+x,1/4-z", "1/4-y,1/4+x,3/4-z", "3/4+x,3/4-z,1/4+y", "1/4+x,1/4-z,3/4+y", "3/4-z,3/4+y,1/4-x", "1/4-z,1/4+y,3/4-x", "3/4+y,3/4-x,1/4+z", "1/4+y,1/4-x,3/4+z", "1/4-x,3/4-z,3/4+y", "3/4-x,1/4-z,1/4+y", "1/4+z,3/4+y,3/4-x", "3/4+z,1/4+y,1/4-x", "1/4-y,3/4-x,3/4+z", "3/4-y,1/4-x,1/4+z", "1/4+x,3/4+z,3/4-y", "3/4+x,1/4+z,1/4-y", "1/4-z,3/4-y,3/4+x", "3/4-z,1/4-y,1/4+x", "1/4+y,3/4+x,3/4-z", "3/4+y,1/4+x,1/4-z", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "-y,-z,-x", "1/2-y,1/2-z,1/2-x"]


hm_notation: P n c a
symmetry_xyz:
["x,y,z", "1/2+x,y,-z", "1/2-x,-y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P -3 1 m
symmetry_xyz:
["x,y,z", "x-y,-y,z", "y,-x+y,-z", "-y,-x,-z", "-x+y,-x,z", "-x,-x+y,z", "-x,-y,-z", "-x+y,y,-z", "-y,x-y,z", "y,x,z", "x-y,x,-z", "x,x-y,-z"]


hm_notation: P -3 c 1
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,-x+y,-z", "-x,-x+y,1/2-z", "-x+y,-x,z", "-x+y,y,1/2+z", "-x,-y,-z", "y,x,1/2-z", "-y,x-y,z", "x,x-y,1/2+z", "x-y,x,-z", "x-y,-y,1/2-z"]


hm_notation: P 63 c m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "x-y,x,1/2+z", "-y,-x,1/2+z", "-y,x-y,z", "x-y,-y,z", "-x,-y,1/2+z", "x,x-y,1/2+z", "-x+y,-x,z", "y,x,z", "y,-x+y,1/2+z", "-x+y,y,1/2+z"]


hm_notation: P 4/n m m %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "1/2+y,1/2+x,-z", "1/2+y,-x,-z", "1/2-y,x,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,z", "-y,-x,-z", "-y,1/2+x,-z", "y,1/2-x,z", "1/2-x,y,z", "1/2+x,-y,-z", "-x,-y,-z"]


hm_notation: P n n m
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "-x,-y,z", "-x,-y,-z"]


hm_notation: P -4 21 m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,-x,-z", "1/2-x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,x,-z", "1/2+x,1/2-y,-z"]


hm_notation: R 3 m
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "x,x-y,z", "2/3+x,1/3+x-y,1/3+z", "1/3+x,2/3+x-y,2/3+z", "-y,-x,z", "2/3-y,1/3-x,1/3+z", "1/3-y,2/3-x,2/3+z", "-x+y,y,z", "2/3-x+y,1/3+y,1/3+z", "1/3-x+y,2/3+y,2/3+z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: P -6 c 2
symmetry_xyz:
["x,y,z", "x,x-y,-z", "-x+y,-x,1/2-z", "-y,-x,1/2+z", "-y,x-y,z", "-x+y,y,-z", "x,y,1/2-z", "x,x-y,1/2+z", "-x+y,-x,z", "-y,-x,-z", "-y,x-y,1/2-z", "-x+y,y,1/2+z"]


hm_notation: P -6 m 2
symmetry_xyz:
["x,y,z", "x,x-y,-z", "-x+y,-x,-z", "-y,-x,z", "-y,x-y,z", "-x+y,y,-z", "x,y,-z", "x,x-y,z", "-x+y,-x,z", "-y,-x,-z", "-y,x-y,-z", "-x+y,y,z"]


hm_notation: I -4 2 d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-y,-x,3/4+z", "-y,1/2-x,1/4+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,1/2+y,1/4-z", "1/2-x,+y,3/4-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "1/2+y,x,3/4+z", "+y,1/2+x,1/4+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,1/2-y,1/4-z", "1/2+x,-y,3/4-z"]


hm_notation: P 4/n n c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "1/2+y,-x,-z", "1/2-y,x,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,1/2+x,-z", "y,1/2-x,z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: F d 3
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+z,1/4+x,-y", "1/4+z,3/4+x,1/2-y", "3/4+z,1/4+x,1/2-y", "3/4+z,3/4+x,-y", "1/4+z,-x,1/4+y", "1/4+z,1/2-x,3/4+y", "3/4+z,-x,3/4+y", "3/4+z,1/2-x,1/4+y", "-z,1/4+x,1/4+y", "-z,3/4+x,3/4+y", "1/2-z,1/4+x,3/4+y", "1/2-z,3/4+x,1/4+y", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,3/4-z,3/4-x", "y,1/4-z,1/4-x", "1/2+y,3/4-z,1/4-x", "1/2+y,1/4-z,3/4-x", "3/4-y,3/4-z,x", "3/4-y,1/4-z,1/2+x", "1/4-y,3/4-z,1/2+x", "1/4-y,1/4-z,x", "3/4-y,z,3/4-x", "3/4-y,1/2+z,1/4-x", "1/4-y,z,1/4-x", "1/4-y,1/2+z,3/4-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "-x,1/4+y,1/4+z", "-x,3/4+y,3/4+z", "1/2-x,1/4+y,3/4+z", "1/2-x,3/4+y,1/4+z", "1/4+x,1/4+y,-z", "1/4+x,3/4+y,1/2-z", "3/4+x,1/4+y,1/2-z", "3/4+x,3/4+y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "3/4-z,3/4-x,y", "3/4-z,1/4-x,1/2+y", "1/4-z,3/4-x,1/2+y", "1/4-z,1/4-x,y", "3/4-z,x,3/4-y", "3/4-z,1/2+x,1/4-y", "1/4-z,x,1/4-y", "1/4-z,1/2+x,3/4-y", "z,3/4-x,3/4-y", "z,1/4-x,1/4-y", "1/2+z,3/4-x,1/4-y", "1/2+z,1/4-x,3/4-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,1/4+z,1/4+x", "-y,3/4+z,3/4+x", "1/2-y,1/4+z,3/4+x", "1/2-y,3/4+z,1/4+x", "1/4+y,1/4+z,-x", "1/4+y,3/4+z,1/2-x", "3/4+y,1/4+z,1/2-x", "3/4+y,3/4+z,-x", "1/4+y,-z,1/4+x", "1/4+y,1/2-z,3/4+x", "3/4+y,-z,3/4+x", "3/4+y,1/2-z,1/4+x", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x", "3/4-x,y,3/4-z", "3/4-x,1/2+y,1/4-z", "1/4-x,y,1/4-z", "1/4-x,1/2+y,3/4-z", "x,3/4-y,3/4-z", "x,1/4-y,1/4-z", "1/2+x,3/4-y,1/4-z", "1/2+x,1/4-y,3/4-z", "3/4-x,3/4-y,z", "3/4-x,1/4-y,1/2+z", "1/4-x,3/4-y,1/2+z", "1/4-x,1/4-y,z"]


hm_notation: P 42/m n m
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "1/2+y,1/2-x,1/2-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "-x,-y,z", "y,x,z", "-y,-x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: I -4 2 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,z", "1/2+y,1/2+x,1/2+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: F d 3 m %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,3/4-x,1/4+y", "3/4+z,1/4-x,3/4+y", "1/4+z,3/4-x,3/4+y", "1/4+z,1/4-x,1/4+y", "-y,1/2+z,1/2-x", "-y,+z,-x", "1/2-y,1/2+z,-x", "1/2-y,+z,1/2-x", "3/4+x,3/4-y,1/4+z", "3/4+x,1/4-y,3/4+z", "1/4+x,3/4-y,3/4+z", "1/4+x,1/4-y,1/4+z", "-z,1/2+x,1/2-y", "-z,+x,-y", "1/2-z,1/2+x,-y", "1/2-z,+x,1/2-y", "3/4+y,3/4-z,1/4+x", "3/4+y,1/4-z,3/4+x", "1/4+y,3/4-z,3/4+x", "1/4+y,1/4-z,1/4+x", "-x,1/2+y,1/2-z", "-x,+y,-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "1/2+x,-z,1/2-y", "1/2+x,1/2-z,-y", "+x,-z,-y", "+x,1/2-z,1/2-y", "3/4-z,3/4+y,1/4+x", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,3/4+x", "1/4-z,1/4+y,1/4+x", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "+y,-x,-z", "+y,1/2-x,1/2-z", "3/4-x,3/4+z,1/4+y", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,3/4+y", "1/4-x,1/4+z,1/4+y", "1/2+z,-y,1/2-x", "1/2+z,1/2-y,-x", "+z,-y,-x", "+z,1/2-y,1/2-x", "3/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,3/4+z", "1/4-y,1/4+x,1/4+z", "x,1/2+z,1/2+y", "x,+z,+y", "1/2+x,1/2+z,+y", "1/2+x,+z,1/2+y", "1/4-z,3/4-y,3/4-x", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,1/4-x", "3/4-z,1/4-y,3/4-x", "y,1/2+x,1/2+z", "y,+x,+z", "1/2+y,1/2+x,+z", "1/2+y,+x,1/2+z", "1/4-x,3/4-z,3/4-y", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,1/4-y", "3/4-x,1/4-z,3/4-y", "z,1/2+y,1/2+x", "z,+y,+x", "1/2+z,1/2+y,+x", "1/2+z,+y,1/2+x", "1/4-y,3/4-x,3/4-z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,3/4-z", "3/4+z,1/4+x,3/4-y", "3/4+z,3/4+x,1/4-y", "1/4+z,1/4+x,1/4-y", "1/4+z,3/4+x,3/4-y", "-y,1/2-z,1/2+x", "-y,-z,+x", "1/2-y,1/2-z,+x", "1/2-y,-z,1/2+x", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "-z,1/2-x,1/2+y", "-z,-x,+y", "1/2-z,1/2-x,+y", "1/2-z,-x,1/2+y", "3/4+y,1/4+z,3/4-x", "3/4+y,3/4+z,1/4-x", "1/4+y,1/4+z,1/4-x", "1/4+y,3/4+z,3/4-x", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z", "1/4-z,3/4+x,3/4+y", "1/4-z,1/4+x,1/4+y", "3/4-z,3/4+x,1/4+y", "3/4-z,1/4+x,3/4+y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "1/4-x,3/4+y,3/4+z", "1/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,1/4+z", "3/4-x,1/4+y,3/4+z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "1/4-y,3/4+z,3/4+x", "1/4-y,1/4+z,1/4+x", "3/4-y,3/4+z,1/4+x", "3/4-y,1/4+z,3/4+x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,1/2+z,-y", "1/2-x,+z,1/2-y", "-x,1/2+z,1/2-y", "-x,+z,-y", "1/4+z,3/4-y,3/4+x", "1/4+z,1/4-y,1/4+x", "3/4+z,3/4-y,1/4+x", "3/4+z,1/4-y,3/4+x", "1/2-y,1/2+x,-z", "1/2-y,+x,1/2-z", "-y,1/2+x,1/2-z", "-y,+x,-z", "1/4+x,3/4-z,3/4+y", "1/4+x,1/4-z,1/4+y", "3/4+x,3/4-z,1/4+y", "3/4+x,1/4-z,3/4+y", "1/2-z,1/2+y,-x", "1/2-z,+y,1/2-x", "-z,1/2+y,1/2-x", "-z,+y,-x", "1/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "3/4+y,3/4-x,1/4+z", "3/4+y,1/4-x,3/4+z", "-x,-z,y", "-x,1/2-z,1/2+y", "1/2-x,-z,1/2+y", "1/2-x,1/2-z,y", "3/4+z,3/4+y,1/4-x", "3/4+z,1/4+y,3/4-x", "1/4+z,3/4+y,3/4-x", "1/4+z,1/4+y,1/4-x", "-y,-x,z", "-y,1/2-x,1/2+z", "1/2-y,-x,1/2+z", "1/2-y,1/2-x,z", "3/4+x,3/4+z,1/4-y", "3/4+x,1/4+z,3/4-y", "1/4+x,3/4+z,3/4-y", "1/4+x,1/4+z,1/4-y", "-z,-y,x", "-z,1/2-y,1/2+x", "1/2-z,-y,1/2+x", "1/2-z,1/2-y,x", "3/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,3/4-z", "1/4+y,1/4+x,1/4-z", "1/4-z,1/4-x,1/4-y", "1/4-z,3/4-x,3/4-y", "3/4-z,1/4-x,3/4-y", "3/4-z,3/4-x,1/4-y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "1/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,3/4-z", "3/4-x,3/4-y,1/4-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "1/4-y,1/4-z,1/4-x", "1/4-y,3/4-z,3/4-x", "3/4-y,1/4-z,3/4-x", "3/4-y,3/4-z,1/4-x"]


hm_notation: P 63 2 2
symmetry_xyz:
["x,y,z", "x,x-y,1/2-z", "x-y,x,1/2+z", "y,x,-z", "-y,x-y,z", "-x+y,y,1/2-z", "-x,-y,1/2+z", "-x,-x+y,-z", "-x+y,-x,z", "-y,-x,1/2-z", "y,-x+y,1/2+z", "x-y,-y,-z"]


hm_notation: P -6 2 c
symmetry_xyz:
["x,y,z", "-x,-x+y,1/2+z", "-x+y,-x,1/2-z", "y,x,-z", "-y,x-y,z", "x-y,-y,1/2+z", "x,y,1/2-z", "-x,-x+y,-z", "-x+y,-x,z", "y,x,1/2+z", "-y,x-y,1/2-z", "x-y,-y,-z"]


hm_notation: I -4 3 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-z,-y", "1/2+x,1/2-z,1/2-y", "z,-y,-x", "1/2+z,1/2-y,1/2-x", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,z,y", "1/2+x,1/2+z,1/2+y", "z,y,x", "1/2+z,1/2+y,1/2+x", "y,x,z", "1/2+y,1/2+x,1/2+z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,z,-y", "1/2-x,1/2+z,1/2-y", "-z,y,-x", "1/2-z,1/2+y,1/2-x", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,-z,y", "1/2-x,1/2-z,1/2+y", "-z,-y,x", "1/2-z,1/2-y,1/2+x", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: R -3 m %var1%
symmetry_xyz:
["x,y,z", "-x,-z,-y", "-z,-x,-y", "y,x,z", "y,z,x", "-z,-y,-x", "-x,-y,-z", "x,z,y", "z,x,y", "-y,-x,-z", "-y,-z,-x", "z,y,x"]


hm_notation: P 4/m b m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "1/2+y,1/2+x,-z", "y,-x,-z", "-y,x,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "1/2-y,1/2-x,-z", "-y,x,-z", "y,-x,z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P m n b
symmetry_xyz:
["x,y,z", "1/2-x,y,z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: P b m n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "x,-y,z", "-x,y,-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: C m m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,z", "1/2-x,1/2+y,z", "-x,-y,z", "1/2-x,1/2-y,z"]


hm_notation: A m m 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,z", "-x,1/2+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: C m m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: B 1 21/d 1
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "3/4-x,1/2+y,3/4-z", "1/4-x,1/2+y,1/4-z", "3/4+x,1/2-y,3/4+z", "1/4+x,1/2-y,1/4+z", "1/2-x,-y,1/2-z", "-x,-y,-z"]


hm_notation: A b a 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,1/2+y,z", "1/2-x,+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: F -4 3 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-z,-y", "x,1/2-z,1/2-y", "1/2+x,-z,1/2-y", "1/2+x,1/2-z,-y", "z,-y,-x", "z,1/2-y,1/2-x", "1/2+z,-y,1/2-x", "1/2+z,1/2-y,-x", "y,-x,-z", "y,1/2-x,1/2-z", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "x,z,y", "x,1/2+z,1/2+y", "1/2+x,z,1/2+y", "1/2+x,1/2+z,y", "z,y,x", "z,1/2+y,1/2+x", "1/2+z,y,1/2+x", "1/2+z,1/2+y,x", "y,x,z", "y,1/2+x,1/2+z", "1/2+y,x,1/2+z", "1/2+y,1/2+x,z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,z,-y", "-x,1/2+z,1/2-y", "1/2-x,z,1/2-y", "1/2-x,1/2+z,-y", "-z,y,-x", "-z,1/2+y,1/2-x", "1/2-z,y,1/2-x", "1/2-z,1/2+y,-x", "-y,x,-z", "-y,1/2+x,1/2-z", "1/2-y,x,1/2-z", "1/2-y,1/2+x,-z", "-x,-z,y", "-x,1/2-z,1/2+y", "1/2-x,-z,1/2+y", "1/2-x,1/2-z,y", "-z,-y,x", "-z,1/2-y,1/2+x", "1/2-z,-y,1/2+x", "1/2-z,1/2-y,x", "-y,-x,z", "-y,1/2-x,1/2+z", "1/2-y,-x,1/2+z", "1/2-y,1/2-x,z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x"]


hm_notation: I a 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+z,x,1/2-y", "+z,1/2+x,-y", "1/2+z,-x,y", "+z,1/2-x,1/2+y", "-z,x,1/2+y", "1/2-z,1/2+x,+y", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "-y,1/2-z,x", "1/2-y,-z,1/2+x", "1/2-y,z,-x", "-y,1/2+z,1/2-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "1/2-z,x,-y", "-z,1/2+x,1/2-y", "z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "1/2-y,1/2+z,x", "-y,+z,1/2+x", "y,1/2+z,-x", "1/2+y,+z,1/2-x", "1/2+y,-z,x", "+y,1/2-z,1/2+x", "-y,-z,-x", "1/2-y,1/2-z,1/2-x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z"]


hm_notation: P m m n
symmetry_xyz:
["x,y,z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2-x,y,z", "1/2+x,-y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,-y,-z"]


hm_notation: A 1 2/a 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P b a m
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "x,y,-z", "-x,-y,z", "-x,-y,-z"]


hm_notation: F -1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: P 4/n
symmetry_xyz:
["x,y,z", "1/2+y,-x,-z", "1/2-y,x,z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-y,1/2+x,-z", "y,1/2-x,z", "-x,-y,-z"]


hm_notation: P 62 2 2
symmetry_xyz:
["x,y,z", "x,x-y,1/3-z", "x-y,x,1/3+z", "y,x,2/3-z", "-y,x-y,2/3+z", "-x+y,y,-z", "-x,-y,z", "-x,-x+y,1/3-z", "-x+y,-x,1/3+z", "-y,-x,2/3-z", "y,-x+y,2/3+z", "x-y,-y,-z"]


hm_notation: R -3 c %var1%
symmetry_xyz:
["x,y,z", "1/2-x,1/2-z,1/2-y", "-z,-x,-y", "1/2+y,1/2+x,1/2+z", "y,z,x", "1/2-z,1/2-y,1/2-x", "-x,-y,-z", "1/2+x,1/2+z,1/2+y", "z,x,y", "1/2-y,1/2-x,1/2-z", "-y,-z,-x", "1/2+z,1/2+y,1/2+x"]


hm_notation: P 43 2 2
symmetry_xyz:
["x,y,z", "y,x,1/4-z", "-y,x,3/4+z", "-x,y,-z", "-x,-y,1/2+z", "-y,-x,3/4-z", "y,-x,1/4+z", "x,-y,1/2-z"]


hm_notation: I m m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: R 3
symmetry_xyz:
["x,y,z", "2/3+x,1/3+y,1/3+z", "1/3+x,2/3+y,2/3+z", "-y,x-y,z", "2/3-y,1/3+x-y,1/3+z", "1/3-y,2/3+x-y,2/3+z", "-x+y,-x,z", "2/3-x+y,1/3-x,1/3+z", "1/3-x+y,2/3-x,2/3+z"]


hm_notation: A b m 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,1/2-y,z", "x,-y,1/2+z", "-x,1/2+y,z", "-x,+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: P 43 21 2
symmetry_xyz:
["x,y,z", "y,x,-z", "1/2-y,1/2+x,3/4+z", "1/2-x,1/2+y,3/4-z", "-x,-y,1/2+z", "-y,-x,1/2-z", "1/2+y,1/2-x,1/4+z", "1/2+x,1/2-y,1/4-z"]


hm_notation: A 1 2/m 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "x,-y,z", "x,1/2-y,1/2+z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: B m m b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "-x,1/2-y,z", "1/2-x,1/2-y,1/2+z", "-x,y,z", "1/2-x,y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: I 41/a m d %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,1/2-x,1/4+z", "1/2-y,-x,3/4+z", "1/2+y,1/2+x,1/2-z", "+y,+x,-z", "1/2+y,1/2-x,1/2-z", "+y,-x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,1/2-y,1/2+z", "+x,-y,+z", "1/2-x,y,3/4-z", "-x,1/2+y,1/4-z", "1/2+x,y,3/4-z", "+x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "1/2+y,x,3/4+z", "+y,1/2+x,1/4+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,1/2-y,1/4-z", "1/2+x,-y,3/4-z", "-x,1/2-y,1/4-z", "1/2-x,-y,3/4-z"]


hm_notation: P 6/m m m
symmetry_xyz:
["x,y,z", "-x,-x+y,z", "x,x-y,-z", "-x+y,-x,-z", "x-y,x,z", "-y,-x,z", "y,x,-z", "y,-x+y,-z", "-y,x-y,z", "x-y,-y,z", "-x+y,y,-z", "x,y,-z", "-x,-y,z", "x,x-y,z", "-x,-x+y,-z", "x-y,x,-z", "-x+y,-x,z", "y,x,z", "-y,-x,-z", "-y,x-y,-z", "y,-x+y,z", "-x+y,y,z", "x-y,-y,-z", "-x,-y,-z"]


hm_notation: P 4/n %var1%
symmetry_xyz:
["x,y,z", "y,-x,-z", "1/2-y,1/2+x,z", "1/2+x,1/2+y,-z", "-x,-y,z", "-y,x,-z", "1/2+y,1/2-x,z", "1/2-x,1/2-y,-z"]


hm_notation: B m a m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "1/2+x,y,-z", "+x,y,1/2-z", "1/2-x,-y,z", "-x,-y,1/2+z", "-x,y,z", "1/2-x,y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z", "1/2+x,-y,z", "+x,-y,1/2+z", "1/2-x,y,-z", "-x,y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: F d d 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/4-x,1/4+y,1/4+z", "1/4-x,3/4+y,3/4+z", "3/4-x,1/4+y,3/4+z", "3/4-x,3/4+y,1/4+z", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z"]


hm_notation: I b a m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 2 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P c a b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: P m 3 n
symmetry_xyz:
["x,y,z", "z,-x,y", "-y,z,-x", "x,-y,z", "-z,x,-y", "y,-z,x", "-x,y,-z", "1/2+x,1/2-z,1/2-y", "1/2-z,1/2+y,1/2+x", "1/2+y,1/2-x,1/2-z", "1/2-x,1/2+z,1/2+y", "1/2+z,1/2-y,1/2-x", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2+z,1/2+y", "1/2-z,1/2-y,1/2-x", "1/2+y,1/2+x,1/2+z", "1/2-x,1/2-z,1/2-y", "1/2+z,1/2+y,1/2+x", "1/2-y,1/2-x,1/2-z", "z,x,-y", "-y,-z,x", "x,y,-z", "-z,-x,y", "y,z,-x", "-x,-y,z", "-z,x,y", "y,-z,-x", "-x,y,z", "z,-x,-y", "-y,z,x", "x,-y,-z", "1/2-x,1/2+z,1/2-y", "1/2+z,1/2-y,1/2+x", "1/2-y,1/2+x,1/2-z", "1/2+x,1/2-z,1/2+y", "1/2-z,1/2+y,1/2-x", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2-z,1/2+y", "1/2+z,1/2+y,1/2-x", "1/2-y,1/2-x,1/2+z", "1/2+x,1/2+z,1/2-y", "1/2-z,1/2-y,1/2+x", "1/2+y,1/2+x,1/2-z", "-z,-x,-y", "y,z,x", "-x,-y,-z", "z,x,y", "-y,-z,-x"]


hm_notation: I m m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: C 1 1 21/d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/4+x,1/4+y,1/2-z", "3/4+x,3/4+y,1/2-z", "1/4-x,1/4-y,1/2+z", "3/4-x,3/4-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P 4/n c c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "1/2+y,-x,-z", "1/2-y,x,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,1/2+x,-z", "y,1/2-x,z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 42/m b c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "y,-x,1/2-z", "-y,x,1/2+z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,x,1/2-z", "y,-x,1/2+z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "-x,-y,-z"]


hm_notation: I m 3 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "z,-x,y", "1/2+z,1/2-x,1/2+y", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "y,-z,x", "1/2+y,1/2-z,1/2+x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-z,-y", "1/2+x,1/2-z,1/2-y", "-z,y,x", "1/2-z,1/2+y,1/2+x", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "-x,z,y", "1/2-x,1/2+z,1/2+y", "z,-y,-x", "1/2+z,1/2-y,1/2-x", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,z,y", "1/2+x,1/2+z,1/2+y", "-z,-y,-x", "1/2-z,1/2-y,1/2-x", "y,x,z", "1/2+y,1/2+x,1/2+z", "-x,-z,-y", "1/2-x,1/2-z,1/2-y", "z,y,x", "1/2+z,1/2+y,1/2+x", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "z,x,-y", "1/2+z,1/2+x,1/2-y", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "y,z,-x", "1/2+y,1/2+z,1/2-x", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-z,x,y", "1/2-z,1/2+x,1/2+y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "-x,y,z", "1/2-x,1/2+y,1/2+z", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "-y,z,x", "1/2-y,1/2+z,1/2+x", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,z,-y", "1/2-x,1/2+z,1/2-y", "z,-y,x", "1/2+z,1/2-y,1/2+x", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "x,-z,y", "1/2+x,1/2-z,1/2+y", "-z,y,-x", "1/2-z,1/2+y,1/2-x", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,-z,y", "1/2-x,1/2-z,1/2+y", "z,y,-x", "1/2+z,1/2+y,1/2-x", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "x,z,-y", "1/2+x,1/2+z,1/2-y", "-z,-y,x", "1/2-z,1/2-y,1/2+x", "y,x,-z", "1/2+y,1/2+x,1/2-z", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "-y,-z,-x", "1/2-y,1/2-z,1/2-x"]


hm_notation: P 42/n n m
symmetry_xyz:
["x,y,z", "-y,-x,z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "y,x,z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: B m a b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "-x,1/2-y,1/2+z", "1/2-x,1/2-y,+z", "-x,y,z", "1/2-x,y,1/2+z", "x,-y,-z", "1/2+x,-y,1/2-z", "x,1/2-y,1/2+z", "1/2+x,1/2-y,+z", "-x,1/2+y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P 4 21 2
symmetry_xyz:
["x,y,z", "y,x,-z", "1/2-y,1/2+x,z", "1/2-x,1/2+y,-z", "-x,-y,z", "-y,-x,-z", "1/2+y,1/2-x,z", "1/2+x,1/2-y,-z"]


hm_notation: F d d d %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "1/4-x,3/4+y,3/4+z", "1/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,1/4+z", "3/4-x,1/4+y,3/4+z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "3/4+x,3/4+y,1/4-z", "3/4+x,1/4+y,3/4-z", "1/4+x,3/4+y,3/4-z", "1/4+x,1/4+y,1/4-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "1/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,3/4-z", "3/4-x,3/4-y,1/4-z"]


hm_notation: P 43 3 2
symmetry_xyz:
["x,y,z", "-z,1/2+x,1/2-y", "-y,1/2+z,1/2-x", "-x,1/2+y,1/2-z", "3/4-x,1/4+z,3/4+y", "3/4-z,1/4+y,3/4+x", "3/4-y,1/4+x,3/4+z", "1/4-x,1/4-z,1/4-y", "1/4-z,1/4-y,1/4-x", "1/4-y,1/4-x,1/4-z", "1/2-z,-x,1/2+y", "1/2-y,-z,1/2+x", "1/2-x,-y,1/2+z", "1/2+z,1/2-x,-y", "1/2+y,1/2-z,-x", "1/2+x,1/2-y,-z", "3/4+x,3/4-z,1/4+y", "3/4+z,3/4-y,1/4+x", "3/4+y,3/4-x,1/4+z", "1/4+x,3/4+z,3/4-y", "1/4+z,3/4+y,3/4-x", "1/4+y,3/4+x,3/4-z", "z,x,y", "y,z,x"]


hm_notation: P b m a
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "1/2+x,y,-z", "1/2-x,-y,z", "x,1/2-y,z", "-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: I 41 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+y,1/2+x,1/2-z", "+y,+x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2-x,y,3/4-z", "-x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "x,1/2-y,1/4-z", "1/2+x,-y,3/4-z"]


hm_notation: P 42/n c m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "1/2+y,1/2+x,-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,z", "-y,-x,-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 42/n
symmetry_xyz:
["x,y,z", "y,1/2-x,1/2-z", "-y,1/2+x,1/2+z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2-y,x,1/2-z", "1/2+y,-x,1/2+z", "-x,-y,-z"]


hm_notation: P 42/n m c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,x,-z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,-x,-z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "1/2+x,1/2-y,1/2-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 41/a %var2%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+y,1/2-x,1/2-z", "+y,-x,-z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,y,3/4-z", "+x,1/2+y,1/4-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,1/2-y,1/4-z", "1/2-x,-y,3/4-z"]


hm_notation: B b m m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,1/2+y,z", "1/2-x,1/2+y,1/2+z", "x,1/2-y,-z", "1/2+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,y,1/2-z", "-x,-y,z", "1/2-x,-y,1/2+z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P m m n %var1%
symmetry_xyz:
["x,y,z", "x,-y,z", "1/2-x,1/2+y,-z", "-x,y,z", "1/2+x,1/2-y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,-z"]


hm_notation: C c m b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "+x,-y,1/2-z", "x,1/2-y,z", "1/2+x,-y,z", "1/2-x,y,-z", "-x,1/2+y,-z", "1/2+x,y,1/2-z", "+x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P n m m
symmetry_xyz:
["x,y,z", "x,y,1/2-z", "-x,-y,1/2+z", "x,1/2-y,z", "-x,1/2+y,-z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P n a a
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: F m m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: P n 3
symmetry_xyz:
["x,y,z", "1/2+z,1/2+x,-y", "1/2+z,-x,1/2+y", "-z,1/2+x,1/2+y", "-z,-x,-y", "y,1/2-z,1/2-x", "1/2-y,1/2-z,x", "1/2-y,z,1/2-x", "y,z,x", "1/2+x,-y,1/2+z", "-x,1/2+y,1/2+z", "1/2+x,1/2+y,-z", "-x,-y,-z", "1/2-z,1/2-x,y", "1/2-z,x,1/2-y", "z,1/2-x,1/2-y", "z,x,y", "-y,1/2+z,1/2+x", "1/2+y,1/2+z,-x", "1/2+y,-z,1/2+x", "-y,-z,-x", "1/2-x,y,1/2-z", "x,1/2-y,1/2-z", "1/2-x,1/2-y,z"]


hm_notation: I 2 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P c a n
symmetry_xyz:
["x,y,z", "-x,y,1/2+z", "x,-y,1/2-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: P 4/n c c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,x,1/2-z", "y,-x,-z", "1/2-y,1/2+x,z", "x,-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,-x,1/2-z", "-y,x,-z", "1/2+y,1/2-x,z", "-x,y,1/2+z", "1/2+x,1/2-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: P 41 3 2
symmetry_xyz:
["x,y,z", "-z,1/2+x,1/2-y", "-y,1/2+z,1/2-x", "-x,1/2+y,1/2-z", "1/4-x,3/4+z,1/4+y", "1/4-z,3/4+y,1/4+x", "1/4-y,3/4+x,1/4+z", "3/4-x,3/4-z,3/4-y", "3/4-z,3/4-y,3/4-x", "3/4-y,3/4-x,3/4-z", "1/2-z,-x,1/2+y", "1/2-y,-z,1/2+x", "1/2-x,-y,1/2+z", "1/2+z,1/2-x,-y", "1/2+y,1/2-z,-x", "1/2+x,1/2-y,-z", "1/4+x,1/4-z,3/4+y", "1/4+z,1/4-y,3/4+x", "1/4+y,1/4-x,3/4+z", "3/4+x,1/4+z,1/4-y", "3/4+z,1/4+y,1/4-x", "3/4+y,1/4+x,1/4-z", "z,x,y", "y,z,x"]


hm_notation: A c m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,-y,1/2+z", "x,1/2-y,+z", "-x,y,1/2-z", "-x,1/2+y,-z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "-x,y,1/2+z", "-x,1/2+y,+z", "x,-y,1/2-z", "x,1/2-y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 42/m c m
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "y,-x,1/2-z", "-y,x,1/2+z", "x,-y,1/2+z", "-x,y,1/2-z", "x,y,-z", "-x,-y,z", "y,x,z", "-y,-x,-z", "-y,x,1/2-z", "y,-x,1/2+z", "-x,y,1/2+z", "x,-y,1/2-z", "-x,-y,-z"]


hm_notation: F d 2 d
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4-x,1/4+y,1/4+z", "1/4-x,3/4+y,3/4+z", "3/4-x,1/4+y,3/4+z", "3/4-x,3/4+y,1/4+z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "-x,1/2+y,1/2-z", "-x,+y,-z"]


hm_notation: B 1 1 2/b
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,1/2-y,z", "1/2-x,1/2-y,1/2+z", "x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P 4/m c c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x,-z", "-y,x,z", "x,-y,1/2+z", "-x,y,1/2-z", "x,y,-z", "-x,-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x,-z", "y,-x,z", "-x,y,1/2+z", "x,-y,1/2-z", "-x,-y,-z"]


hm_notation: P 2 3
symmetry_xyz:
["x,y,z", "-z,-x,y", "-z,x,-y", "z,-x,-y", "z,x,y", "y,-z,-x", "-y,-z,x", "-y,z,-x", "y,z,x", "-x,y,-z", "x,-y,-z", "-x,-y,z"]


hm_notation: A m a 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,z", "1/2-x,1/2+y,1/2+z", "-x,-y,z", "-x,1/2-y,1/2+z"]


hm_notation: P 42/m m c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "y,-x,1/2-z", "-y,x,1/2+z", "x,-y,z", "-x,y,-z", "x,y,-z", "-x,-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,x,1/2-z", "y,-x,1/2+z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: P 42/n m c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,-z", "1/2+y,-x,-z", "1/2-y,x,1/2+z", "x,1/2-y,z", "-x,1/2+y,1/2-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,z", "y,x,1/2+z", "-y,-x,-z", "-y,1/2+x,-z", "y,1/2-x,1/2+z", "1/2-x,y,z", "1/2+x,-y,1/2-z", "-x,-y,1/2-z"]


hm_notation: I m a 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2-x,1/2-y,z", "-x,-y,1/2+z"]


hm_notation: F d 3 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+z,1/4+x,1/4-y", "1/4+z,3/4+x,3/4-y", "3/4+z,1/4+x,3/4-y", "3/4+z,3/4+x,1/4-y", "1/4+z,1/4-x,1/4+y", "1/4+z,3/4-x,3/4+y", "3/4+z,1/4-x,3/4+y", "3/4+z,3/4-x,1/4+y", "1/4-z,1/4+x,1/4+y", "1/4-z,3/4+x,3/4+y", "3/4-z,1/4+x,3/4+y", "3/4-z,3/4+x,1/4+y", "1/4-z,1/4-x,1/4-y", "1/4-z,3/4-x,3/4-y", "3/4-z,1/4-x,3/4-y", "3/4-z,3/4-x,1/4-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/4-x,1/4+y,1/4+z", "1/4-x,3/4+y,3/4+z", "3/4-x,1/4+y,3/4+z", "3/4-x,3/4+y,1/4+z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,3/4-z", "3/4-x,3/4-y,1/4-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "1/4-y,1/4+z,1/4+x", "1/4-y,3/4+z,3/4+x", "3/4-y,1/4+z,3/4+x", "3/4-y,3/4+z,1/4+x", "1/4+y,1/4+z,1/4-x", "1/4+y,3/4+z,3/4-x", "3/4+y,1/4+z,3/4-x", "3/4+y,3/4+z,1/4-x", "1/4+y,1/4-z,1/4+x", "1/4+y,3/4-z,3/4+x", "3/4+y,1/4-z,3/4+x", "3/4+y,3/4-z,1/4+x", "1/4-y,1/4-z,1/4-x", "1/4-y,3/4-z,3/4-x", "3/4-y,1/4-z,3/4-x", "3/4-y,3/4-z,1/4-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: I 1 1 2/a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-x,-y,z", "-x,1/2-y,1/2+z", "1/2+x,y,-z", "+x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: F 41 3 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,1/2+x,1/2-y", "-z,+x,-y", "1/2-z,1/2+x,-y", "1/2-z,+x,1/2-y", "-y,1/2+z,1/2-x", "-y,+z,-x", "1/2-y,1/2+z,-x", "1/2-y,+z,1/2-x", "-x,1/2+y,1/2-z", "-x,+y,-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "3/4-x,3/4+z,1/4+y", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,3/4+y", "1/4-x,1/4+z,1/4+y", "3/4-z,3/4+y,1/4+x", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,3/4+x", "1/4-z,1/4+y,1/4+x", "3/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,3/4+z", "1/4-y,1/4+x,1/4+z", "1/4-x,3/4-z,3/4-y", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,1/4-y", "3/4-x,1/4-z,3/4-y", "1/4-z,3/4-y,3/4-x", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,1/4-x", "3/4-z,1/4-y,3/4-x", "1/4-y,3/4-x,3/4-z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,3/4-z", "-z,1/2-x,1/2+y", "-z,-x,+y", "1/2-z,1/2-x,+y", "1/2-z,-x,1/2+y", "-y,1/2-z,1/2+x", "-y,-z,+x", "1/2-y,1/2-z,+x", "1/2-y,-z,1/2+x", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "1/4+x,3/4-z,3/4+y", "1/4+x,1/4-z,1/4+y", "3/4+x,3/4-z,1/4+y", "3/4+x,1/4-z,3/4+y", "1/4+z,3/4-y,3/4+x", "1/4+z,1/4-y,1/4+x", "3/4+z,3/4-y,1/4+x", "3/4+z,1/4-y,3/4+x", "1/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "3/4+y,3/4-x,1/4+z", "3/4+y,1/4-x,3/4+z", "3/4+x,3/4+z,1/4-y", "3/4+x,1/4+z,3/4-y", "1/4+x,3/4+z,3/4-y", "1/4+x,1/4+z,1/4-y", "3/4+z,3/4+y,1/4-x", "3/4+z,1/4+y,3/4-x", "1/4+z,3/4+y,3/4-x", "1/4+z,1/4+y,1/4-x", "3/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,3/4-z", "1/4+y,1/4+x,1/4-z", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x"]


hm_notation: I 4 2 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,x,-z", "1/2+y,1/2+x,1/2-z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: I 4 3 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,z,y", "1/2-x,1/2+z,1/2+y", "-z,y,x", "1/2-z,1/2+y,1/2+x", "-y,x,z", "1/2-y,1/2+x,1/2+z", "-x,-z,-y", "1/2-x,1/2-z,1/2-y", "-z,-y,-x", "1/2-z,1/2-y,1/2-x", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,-z,y", "1/2+x,1/2-z,1/2+y", "z,-y,x", "1/2+z,1/2-y,1/2+x", "y,-x,z", "1/2+y,1/2-x,1/2+z", "x,z,-y", "1/2+x,1/2+z,1/2-y", "z,y,-x", "1/2+z,1/2+y,1/2-x", "y,x,-z", "1/2+y,1/2+x,1/2-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: P c n n
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,y,1/2+z", "x,-y,1/2-z", "-x,-y,-z"]


hm_notation: I -4 c 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,x,1/2-z", "1/2+y,1/2+x,-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,-x,1/2-z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z"]


hm_notation: C 2 2 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,-z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P n a n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,z", "1/2-x,y,-z", "-x,-y,-z"]


hm_notation: P 41 2 2
symmetry_xyz:
["x,y,z", "y,x,3/4-z", "-y,x,1/4+z", "-x,y,-z", "-x,-y,1/2+z", "-y,-x,1/4-z", "y,-x,3/4+z", "x,-y,1/2-z"]


hm_notation: P 42 n m
symmetry_xyz:
["x,y,z", "-y,-x,z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "y,x,z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,1/2+z"]


hm_notation: I -4 m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "y,x,-z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2+y,1/2-x,1/2-z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-y,1/2+x,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z"]


hm_notation: C c c a %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,1/2-z", "-x,1/2+y,1/2+z", "1/2-x,+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "x,1/2+y,-z", "1/2+x,+y,-z", "-x,1/2-y,z", "1/2-x,-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: I b c a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P b n a
symmetry_xyz:
["x,y,z", "-x,1/2+y,z", "x,1/2-y,-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: P m n a
symmetry_xyz:
["x,y,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,y,z", "x,-y,-z", "1/2+x,y,1/2-z", "1/2-x,-y,1/2+z", "-x,-y,-z"]


hm_notation: I 4 m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,-x,z", "1/2-y,1/2-x,1/2+z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,x,z", "1/2+y,1/2+x,1/2+z", "y,-x,z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z"]


hm_notation: I 41/a c d %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/4-y,3/4-x,3/4+z", "3/4-y,1/4-x,1/4+z", "1/4+y,3/4+x,3/4-z", "3/4+y,1/4+x,1/4-z", "1/4+y,3/4-x,1/4-z", "3/4+y,1/4-x,3/4-z", "1/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "+x,1/2+y,-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/4+y,1/4+x,1/4+z", "3/4+y,3/4+x,3/4+z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/4-y,1/4+x,3/4-z", "3/4-y,3/4+x,1/4-z", "1/4+y,1/4-x,3/4+z", "3/4+y,3/4-x,1/4+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I m 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "z,x,-y", "1/2+z,1/2+x,1/2-y", "z,-x,y", "1/2+z,1/2-x,1/2+y", "-z,x,y", "1/2-z,1/2+x,1/2+y", "-z,-x,-y", "1/2-z,1/2-x,1/2-y", "y,-z,-x", "1/2+y,1/2-z,1/2-x", "-y,-z,x", "1/2-y,1/2-z,1/2+x", "-y,z,-x", "1/2-y,1/2+z,1/2-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z", "-z,-x,y", "1/2-z,1/2-x,1/2+y", "-z,x,-y", "1/2-z,1/2+x,1/2-y", "z,-x,-y", "1/2+z,1/2-x,1/2-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "-y,z,x", "1/2-y,1/2+z,1/2+x", "y,z,-x", "1/2+y,1/2+z,1/2-x", "y,-z,x", "1/2+y,1/2-z,1/2+x", "-y,-z,-x", "1/2-y,1/2-z,1/2-x", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: P m a b
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "x,1/2+y,-z", "-x,1/2-y,z", "1/2-x,y,z", "1/2+x,-y,-z", "-x,-y,-z"]


hm_notation: P 42/n n m %var1%
symmetry_xyz:
["x,y,z", "-y,-x,z", "y,x,-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2+y,1/2+x,z", "1/2-y,1/2-x,-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P m c b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: P 4/m n c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "-y,x,z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "y,-x,z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: F m m 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: I m m a %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,-z", "x,1/2+y,1/2-z", "1/2+x,+y,-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,1/2-y,1/2-z", "1/2-x,-y,-z"]


hm_notation: I 21 21 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "1/2+x,-y,-z", "+x,1/2-y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z"]


hm_notation: I 2 m b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2+y,1/2-z", "1/2+x,+y,-z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "x,1/2-y,1/2-z", "1/2+x,-y,-z"]


hm_notation: C m m a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2+x,-y,z", "+x,1/2-y,z", "1/2-x,y,-z", "-x,1/2+y,-z", "-x,y,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2-y,-z", "1/2+x,y,-z", "+x,1/2+y,-z", "1/2-x,-y,z", "-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: I 21 3
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "-z,1/2+x,1/2-y", "1/2-z,+x,-y", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "z,x,y", "1/2+z,1/2+x,1/2+y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2-y,-z,1/2+x", "-y,1/2-z,+x", "-y,1/2+z,1/2-x", "1/2-y,+z,-x", "y,z,x", "1/2+y,1/2+z,1/2+x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z"]


hm_notation: P -4 n 2
symmetry_xyz:
["x,y,z", "1/2+y,1/2+x,1/2-z", "y,-x,-z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2-y,1/2-x,1/2-z", "-y,x,-z", "1/2-x,1/2+y,1/2+z"]


hm_notation: B m 2 m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,y,z", "1/2-x,y,1/2+z", "x,y,-z", "1/2+x,y,1/2-z", "-x,y,-z", "1/2-x,y,1/2-z"]


hm_notation: A m m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "-x,y,z", "-x,1/2+y,1/2+z", "x,-y,-z", "x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: C m 2 a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2-x,y,z", "-x,1/2+y,z", "1/2+x,y,-z", "+x,1/2+y,-z", "-x,y,-z", "1/2-x,1/2+y,-z"]


hm_notation: A 2 m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "x,-y,z", "x,1/2-y,1/2+z", "x,-y,-z", "x,1/2-y,1/2-z"]


hm_notation: A b m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,1/2+y,-z", "x,+y,1/2-z", "-x,1/2-y,z", "-x,-y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "-x,1/2+y,z", "-x,+y,1/2+z", "x,1/2-y,-z", "x,-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I m 2 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,y,-z", "1/2-x,1/2+y,1/2-z"]


hm_notation: F 2 3
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: P b a n
symmetry_xyz:
["x,y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2-x,1/2-y,-z"]


hm_notation: P -4 b 2
symmetry_xyz:
["x,y,z", "1/2+y,1/2+x,-z", "y,-x,-z", "1/2+x,1/2-y,z", "-x,-y,z", "1/2-y,1/2-x,-z", "-y,x,-z", "1/2-x,1/2+y,z"]


hm_notation: C c m 21
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,z", "1/2+x,1/2-y,z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z"]


hm_notation: I m a m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,1/2+z", "1/2-x,1/2-y,+z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P m 3
symmetry_xyz:
["x,y,z", "z,x,-y", "z,-x,y", "-z,x,y", "-z,-x,-y", "y,-z,-x", "-y,-z,x", "-y,z,-x", "y,z,x", "x,-y,z", "-x,y,z", "x,y,-z", "-x,-y,-z", "-z,-x,y", "-z,x,-y", "z,-x,-y", "z,x,y", "-y,z,x", "y,z,-x", "y,-z,x", "-y,-z,-x", "-x,y,-z", "x,-y,-z", "-x,-y,z"]


hm_notation: I 1 1 2/b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P n 3 %var1%
symmetry_xyz:
["x,y,z", "1/2+z,1/2+x,1/2-y", "1/2+z,1/2-x,1/2+y", "1/2-z,1/2+x,1/2+y", "1/2-z,1/2-x,1/2-y", "y,-z,-x", "-y,-z,x", "-y,z,-x", "y,z,x", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2-z", "-z,-x,y", "-z,x,-y", "z,-x,-y", "z,x,y", "1/2-y,1/2+z,1/2+x", "1/2+y,1/2+z,1/2-x", "1/2+y,1/2-z,1/2+x", "1/2-y,1/2-z,1/2-x", "-x,y,-z", "x,-y,-z", "-x,-y,z"]


hm_notation: P n c b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2+z", "x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: A m m a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,-y,z", "1/2-x,1/2-y,1/2+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I 2 c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "x,y,1/2-z", "1/2+x,1/2+y,-z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: I 4
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,x,z", "1/2-y,1/2+x,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "y,-x,z", "1/2+y,1/2-x,1/2+z"]


hm_notation: I 41 3 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-z,1/2+x,1/2-y", "1/2-z,+x,-y", "-y,1/2+z,1/2-x", "1/2-y,+z,-x", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "3/4-x,1/4+z,3/4+y", "1/4-x,3/4+z,1/4+y", "3/4-z,1/4+y,3/4+x", "1/4-z,3/4+y,1/4+x", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,1/4+z", "1/4-x,1/4-z,1/4-y", "3/4-x,3/4-z,3/4-y", "1/4-z,1/4-y,1/4-x", "3/4-z,3/4-y,3/4-x", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/2-z,-x,1/2+y", "-z,1/2-x,+y", "1/2-y,-z,1/2+x", "-y,1/2-z,+x", "1/2-x,-y,1/2+z", "-x,1/2-y,+z", "1/2+z,1/2-x,-y", "+z,-x,1/2-y", "1/2+y,1/2-z,-x", "+y,-z,1/2-x", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "3/4+x,3/4-z,1/4+y", "1/4+x,1/4-z,3/4+y", "3/4+z,3/4-y,1/4+x", "1/4+z,1/4-y,3/4+x", "3/4+y,3/4-x,1/4+z", "1/4+y,1/4-x,3/4+z", "1/4+x,3/4+z,3/4-y", "3/4+x,1/4+z,1/4-y", "1/4+z,3/4+y,3/4-x", "3/4+z,1/4+y,1/4-x", "1/4+y,3/4+x,3/4-z", "3/4+y,1/4+x,1/4-z", "z,x,y", "1/2+z,1/2+x,1/2+y", "y,z,x", "1/2+y,1/2+z,1/2+x"]


hm_notation: P 42/n b c
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "y,x,1/2-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "1/2+x,-y,z", "1/2-x,y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "-x,1/2+y,z", "x,1/2-y,-z", "-x,-y,-z"]


hm_notation: A m a a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,-z", "1/2+x,1/2+y,1/2-z", "1/2-x,-y,z", "1/2-x,1/2-y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "1/2-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,y,z", "-x,1/2+y,1/2+z", "x,-y,-z", "x,1/2-y,1/2-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 63 %var1%
symmetry_xyz:
["x,y,z", "2/3+x-y,1/3+x,1/2+z", "-y,+x-y,z", "2/3-x,1/3-y,1/2+z", "-x+y,-x,z", "2/3+y,1/3-x+y,1/2+z"]


hm_notation: P b n n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,1/2+y,z", "x,1/2-y,-z", "-x,-y,-z"]


hm_notation: B b a 2
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "1/2-x,1/2+y,z", "-x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "+x,1/2-y,1/2+z", "-x,-y,z", "1/2-x,-y,1/2+z"]


hm_notation: I m c m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2-x,y,z", "-x,1/2+y,1/2+z", "1/2+x,-y,-z", "+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2-x,1/2-y,1/2+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: C c m b %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2-x,y,1/2+z", "-x,1/2+y,1/2+z", "1/2+x,-y,1/2-z", "+x,1/2-y,1/2-z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "1/2+x,y,1/2-z", "+x,1/2+y,1/2-z", "1/2-x,-y,1/2+z", "-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: P m n m
symmetry_xyz:
["x,y,z", "1/2-x,y,z", "1/2+x,-y,-z", "x,y,1/2-z", "-x,-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,-y,-z"]


hm_notation: F 1 1 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: B b 21 m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,1/2+y,z", "1/2-x,1/2+y,1/2+z", "x,y,-z", "1/2+x,y,1/2-z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z"]


hm_notation: B 1 1 2/m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "-x,-y,z", "1/2-x,-y,1/2+z", "x,y,-z", "1/2+x,y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: F d 3 c
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,-x,3/4+y", "3/4+z,1/2-x,1/4+y", "1/4+z,-x,1/4+y", "1/4+z,1/2-x,3/4+y", "3/4-y,1/2+z,1/4-x", "3/4-y,+z,3/4-x", "1/4-y,1/2+z,3/4-x", "1/4-y,+z,1/4-x", "1/4+x,1/2-y,3/4+z", "1/4+x,-y,1/4+z", "3/4+x,1/2-y,1/4+z", "3/4+x,-y,3/4+z", "3/4-z,x,3/4-y", "3/4-z,1/2+x,1/4-y", "1/4-z,x,1/4-y", "1/4-z,1/2+x,3/4-y", "3/4+y,1/2-z,1/4+x", "3/4+y,-z,3/4+x", "1/4+y,1/2-z,3/4+x", "1/4+y,-z,1/4+x", "1/4-x,1/2+y,3/4-z", "1/4-x,+y,1/4-z", "3/4-x,1/2+y,1/4-z", "3/4-x,+y,3/4-z", "1/2+x,1/4-z,1/4-y", "1/2+x,3/4-z,3/4-y", "+x,1/4-z,3/4-y", "+x,3/4-z,1/4-y", "-z,1/4+y,3/4+x", "-z,3/4+y,1/4+x", "1/2-z,1/4+y,1/4+x", "1/2-z,3/4+y,3/4+x", "y,3/4-x,1/4-z", "y,1/4-x,3/4-z", "1/2+y,3/4-x,3/4-z", "1/2+y,1/4-x,1/4-z", "1/2-x,1/4+z,1/4+y", "1/2-x,3/4+z,3/4+y", "-x,1/4+z,3/4+y", "-x,3/4+z,1/4+y", "z,1/4-y,3/4-x", "z,3/4-y,1/4-x", "1/2+z,1/4-y,1/4-x", "1/2+z,3/4-y,3/4-x", "-y,3/4+x,1/4+z", "-y,1/4+x,3/4+z", "1/2-y,3/4+x,3/4+z", "1/2-y,1/4+x,1/4+z", "x,1/2+z,y", "x,+z,1/2+y", "1/2+x,1/2+z,1/2+y", "1/2+x,+z,y", "1/2-z,1/2-y,1/2-x", "1/2-z,-y,-x", "-z,1/2-y,-x", "-z,-y,1/2-x", "1/2+y,x,z", "1/2+y,1/2+x,1/2+z", "+y,x,1/2+z", "+y,1/2+x,z", "-x,1/2-z,-y", "-x,-z,1/2-y", "1/2-x,1/2-z,1/2-y", "1/2-x,-z,-y", "1/2+z,1/2+y,1/2+x", "1/2+z,+y,+x", "+z,1/2+y,+x", "+z,+y,1/2+x", "1/2-y,-x,-z", "1/2-y,1/2-x,1/2-z", "-y,-x,1/2-z", "-y,1/2-x,-z", "3/4+z,1/4+x,1/2-y", "3/4+z,3/4+x,-y", "1/4+z,1/4+x,-y", "1/4+z,3/4+x,1/2-y", "3/4-y,3/4-z,x", "3/4-y,1/4-z,1/2+x", "1/4-y,3/4-z,1/2+x", "1/4-y,1/4-z,x", "1/4+x,3/4+y,1/2-z", "1/4+x,1/4+y,-z", "3/4+x,3/4+y,-z", "3/4+x,1/4+y,1/2-z", "3/4-z,1/4-x,1/2+y", "3/4-z,3/4-x,+y", "1/4-z,1/4-x,+y", "1/4-z,3/4-x,1/2+y", "3/4+y,3/4+z,-x", "3/4+y,1/4+z,1/2-x", "1/4+y,3/4+z,1/2-x", "1/4+y,1/4+z,-x", "1/4-x,3/4-y,1/2+z", "1/4-x,1/4-y,+z", "3/4-x,3/4-y,+z", "3/4-x,1/4-y,1/2+z", "1/2-z,3/4+x,1/4+y", "1/2-z,1/4+x,3/4+y", "-z,3/4+x,3/4+y", "-z,1/4+x,1/4+y", "1/2+y,1/4-z,3/4-x", "1/2+y,3/4-z,1/4-x", "+y,1/4-z,1/4-x", "+y,3/4-z,3/4-x", "-x,1/4+y,1/4+z", "-x,3/4+y,3/4+z", "1/2-x,1/4+y,3/4+z", "1/2-x,3/4+y,1/4+z", "1/2+z,3/4-x,1/4-y", "1/2+z,1/4-x,3/4-y", "+z,3/4-x,3/4-y", "+z,1/4-x,1/4-y", "1/2-y,1/4+z,3/4+x", "1/2-y,3/4+z,1/4+x", "-y,1/4+z,1/4+x", "-y,3/4+z,3/4+x", "x,1/4-y,1/4-z", "x,3/4-y,3/4-z", "1/2+x,1/4-y,3/4-z", "1/2+x,3/4-y,1/4-z", "3/4-x,1/2+z,3/4-y", "3/4-x,+z,1/4-y", "1/4-x,1/2+z,1/4-y", "1/4-x,+z,3/4-y", "1/4+z,1/2-y,1/4+x", "1/4+z,-y,3/4+x", "3/4+z,1/2-y,3/4+x", "3/4+z,-y,1/4+x", "1/4-y,x,3/4-z", "1/4-y,1/2+x,1/4-z", "3/4-y,x,1/4-z", "3/4-y,1/2+x,3/4-z", "3/4+x,1/2-z,3/4+y", "3/4+x,-z,1/4+y", "1/4+x,1/2-z,1/4+y", "1/4+x,-z,3/4+y", "1/4-z,1/2+y,1/4-x", "1/4-z,+y,3/4-x", "3/4-z,1/2+y,3/4-x", "3/4-z,+y,1/4-x", "1/4+y,-x,3/4+z", "1/4+y,1/2-x,1/4+z", "3/4+y,-x,1/4+z", "3/4+y,1/2-x,3/4+z", "1/4-x,1/4-z,1/2+y", "1/4-x,3/4-z,+y", "3/4-x,1/4-z,+y", "3/4-x,3/4-z,1/2+y", "3/4+z,1/4+y,-x", "3/4+z,3/4+y,1/2-x", "1/4+z,1/4+y,1/2-x", "1/4+z,3/4+y,-x", "3/4-y,3/4-x,1/2+z", "3/4-y,1/4-x,+z", "1/4-y,3/4-x,+z", "1/4-y,1/4-x,1/2+z", "1/4+x,1/4+z,1/2-y", "1/4+x,3/4+z,-y", "3/4+x,1/4+z,-y", "3/4+x,3/4+z,1/2-y", "3/4-z,1/4-y,x", "3/4-z,3/4-y,1/2+x", "1/4-z,1/4-y,1/2+x", "1/4-z,3/4-y,x", "3/4+y,3/4+x,1/2-z", "3/4+y,1/4+x,-z", "1/4+y,3/4+x,-z", "1/4+y,1/4+x,1/2-z", "1/2-z,1/2-x,-y", "1/2-z,-x,1/2-y", "-z,1/2-x,1/2-y", "-z,-x,-y", "1/2+y,z,1/2+x", "1/2+y,1/2+z,+x", "+y,z,+x", "+y,1/2+z,1/2+x", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "1/2+z,1/2+x,y", "1/2+z,+x,1/2+y", "+z,1/2+x,1/2+y", "+z,+x,y", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x", "-y,-z,-x", "-y,1/2-z,1/2-x"]


hm_notation: P 42/n %var1%
symmetry_xyz:
["x,y,z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P b c b
symmetry_xyz:
["x,y,z", "-x,1/2+y,z", "x,1/2-y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "x,-y,1/2+z", "-x,y,1/2-z", "-x,-y,-z"]


hm_notation: P n c m
symmetry_xyz:
["x,y,z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "x,y,-z", "-x,-y,z", "x,1/2-y,1/2+z", "-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: C -4 2 b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2+y,x,z", "+y,1/2+x,z", "1/2-x,y,-z", "-x,1/2+y,-z", "1/2-y,-x,z", "-y,1/2-x,z", "1/2+x,-y,-z", "+x,1/2-y,-z", "y,-x,-z", "1/2+y,1/2-x,-z", "-x,-y,z", "1/2-x,1/2-y,z", "-y,x,-z", "1/2-y,1/2+x,-z"]


hm_notation: P n 3 m
symmetry_xyz:
["x,y,z", "1/2+z,1/2-x,1/2+y", "-y,z,-x", "1/2+x,1/2-y,1/2+z", "-z,x,-y", "1/2+y,1/2-z,1/2+x", "-x,y,-z", "x,-z,-y", "1/2-z,1/2+y,1/2+x", "y,-x,-z", "1/2-x,1/2+z,1/2+y", "z,-y,-x", "1/2-y,1/2+x,1/2+z", "x,z,y", "1/2-z,1/2-y,1/2-x", "y,x,z", "1/2-x,1/2-z,1/2-y", "z,y,x", "1/2-y,1/2-x,1/2-z", "1/2+z,1/2+x,1/2-y", "-y,-z,x", "1/2+x,1/2+y,1/2-z", "-z,-x,y", "1/2+y,1/2+z,1/2-x", "-x,-y,z", "1/2-z,1/2+x,1/2+y", "y,-z,-x", "1/2-x,1/2+y,1/2+z", "z,-x,-y", "1/2-y,1/2+z,1/2+x", "x,-y,-z", "-x,z,-y", "1/2+z,1/2-y,1/2+x", "-y,x,-z", "1/2+x,1/2-z,1/2+y", "-z,y,-x", "1/2+y,1/2-x,1/2+z", "-x,-z,y", "1/2+z,1/2+y,1/2-x", "-y,-x,z", "1/2+x,1/2+z,1/2-y", "-z,-y,x", "1/2+y,1/2+x,1/2-z", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2-y,1/2-z,1/2-x"]


hm_notation: P n 3 m %var1%
symmetry_xyz:
["x,y,z", "1/2+z,-x,1/2+y", "1/2-y,z,1/2-x", "1/2+x,-y,1/2+z", "1/2-z,x,1/2-y", "1/2+y,-z,1/2+x", "1/2-x,y,1/2-z", "x,1/2-z,1/2-y", "-z,1/2+y,1/2+x", "y,1/2-x,1/2-z", "-x,1/2+z,1/2+y", "z,1/2-y,1/2-x", "-y,1/2+x,1/2+z", "x,z,y", "-z,-y,-x", "y,x,z", "-x,-z,-y", "z,y,x", "-y,-x,-z", "1/2+z,1/2+x,-y", "1/2-y,1/2-z,x", "1/2+x,1/2+y,-z", "1/2-z,1/2-x,y", "1/2+y,1/2+z,-x", "1/2-x,1/2-y,z", "-z,1/2+x,1/2+y", "y,1/2-z,1/2-x", "-x,1/2+y,1/2+z", "z,1/2-x,1/2-y", "-y,1/2+z,1/2+x", "x,1/2-y,1/2-z", "1/2-x,z,1/2-y", "1/2+z,-y,1/2+x", "1/2-y,x,1/2-z", "1/2+x,-z,1/2+y", "1/2-z,y,1/2-x", "1/2+y,-x,1/2+z", "1/2-x,1/2-z,y", "1/2+z,1/2+y,-x", "1/2-y,1/2-x,z", "1/2+x,1/2+z,-y", "1/2-z,1/2-y,x", "1/2+y,1/2+x,-z", "-z,-x,-y", "y,z,x", "-x,-y,-z", "z,x,y", "-y,-z,-x"]


hm_notation: C c m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "x,-y,1/2-z", "1/2+x,1/2-y,1/2-z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "x,y,1/2-z", "1/2+x,1/2+y,1/2-z", "-x,-y,1/2+z", "1/2-x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F m 2 m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z"]


hm_notation: F m 3
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "z,x,-y", "z,1/2+x,1/2-y", "1/2+z,x,1/2-y", "1/2+z,1/2+x,-y", "z,-x,y", "z,1/2-x,1/2+y", "1/2+z,-x,1/2+y", "1/2+z,1/2-x,y", "-z,x,y", "-z,1/2+x,1/2+y", "1/2-z,x,1/2+y", "1/2-z,1/2+x,y", "-z,-x,-y", "-z,1/2-x,1/2-y", "1/2-z,-x,1/2-y", "1/2-z,1/2-x,-y", "y,-z,-x", "y,1/2-z,1/2-x", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "-y,-z,x", "-y,1/2-z,1/2+x", "1/2-y,-z,1/2+x", "1/2-y,1/2-z,x", "-y,z,-x", "-y,1/2+z,1/2-x", "1/2-y,z,1/2-x", "1/2-y,1/2+z,-x", "y,z,x", "y,1/2+z,1/2+x", "1/2+y,z,1/2+x", "1/2+y,1/2+z,x", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,z", "-x,1/2+y,1/2+z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "-z,-x,y", "-z,1/2-x,1/2+y", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,y", "-z,x,-y", "-z,1/2+x,1/2-y", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "z,-x,-y", "z,1/2-x,1/2-y", "1/2+z,-x,1/2-y", "1/2+z,1/2-x,-y", "z,x,y", "z,1/2+x,1/2+y", "1/2+z,x,1/2+y", "1/2+z,1/2+x,y", "-y,z,x", "-y,1/2+z,1/2+x", "1/2-y,z,1/2+x", "1/2-y,1/2+z,x", "y,z,-x", "y,1/2+z,1/2-x", "1/2+y,z,1/2-x", "1/2+y,1/2+z,-x", "y,-z,x", "y,1/2-z,1/2+x", "1/2+y,-z,1/2+x", "1/2+y,1/2-z,x", "-y,-z,-x", "-y,1/2-z,1/2-x", "1/2-y,-z,1/2-x", "1/2-y,1/2-z,-x", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,z", "-x,1/2-y,1/2+z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,z"]


hm_notation: P b a n %var1%
symmetry_xyz:
["x,y,z", "1/2+x,-y,z", "1/2-x,y,-z", "-x,1/2+y,z", "x,1/2-y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,-y,-z"]


hm_notation: P n 3 n
symmetry_xyz:
["x,y,z", "1/2+z,1/2-x,1/2+y", "-y,z,-x", "1/2+x,1/2-y,1/2+z", "-z,x,-y", "1/2+y,1/2-z,1/2+x", "-x,y,-z", "1/2+x,1/2-z,1/2-y", "-z,y,x", "1/2+y,1/2-x,1/2-z", "-x,z,y", "1/2+z,1/2-y,1/2-x", "-y,x,z", "1/2+x,1/2+z,1/2+y", "-z,-y,-x", "1/2+y,1/2+x,1/2+z", "-x,-z,-y", "1/2+z,1/2+y,1/2+x", "-y,-x,-z", "1/2+z,1/2+x,1/2-y", "-y,-z,x", "1/2+x,1/2+y,1/2-z", "-z,-x,y", "1/2+y,1/2+z,1/2-x", "-x,-y,z", "1/2-z,1/2+x,1/2+y", "y,-z,-x", "1/2-x,1/2+y,1/2+z", "z,-x,-y", "1/2-y,1/2+z,1/2+x", "x,-y,-z", "1/2-x,1/2+z,1/2-y", "z,-y,x", "1/2-y,1/2+x,1/2-z", "x,-z,y", "1/2-z,1/2+y,1/2-x", "y,-x,z", "1/2-x,1/2-z,1/2+y", "z,y,-x", "1/2-y,1/2-x,1/2+z", "x,z,-y", "1/2-z,1/2-y,1/2+x", "y,x,-z", "1/2-z,1/2-x,1/2-y", "y,z,x", "1/2-x,1/2-y,1/2-z", "z,x,y", "1/2-y,1/2-z,1/2-x"]


hm_notation: C m 2 m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,y,z", "1/2-x,1/2+y,z", "x,y,-z", "1/2+x,1/2+y,-z", "-x,y,-z", "1/2-x,1/2+y,-z"]


hm_notation: P m a n
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "-x,y,z", "x,-y,-z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: P 4/n b m
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,x,-z", "1/2+y,1/2-x,-z", "-y,x,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,-x,-z", "1/2-y,1/2+x,-z", "y,-x,z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F 1 2/m 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: B 1 1 21/d
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "3/4-x,3/4-y,1/2+z", "1/4-x,3/4-y,+z", "3/4+x,3/4+y,1/2-z", "1/4+x,3/4+y,-z", "1/2-x,1/2-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 6/m
symmetry_xyz:
["x,y,z", "-x+y,-x,-z", "x-y,x,z", "y,-x+y,-z", "-y,x-y,z", "x,y,-z", "-x,-y,z", "x-y,x,-z", "-x+y,-x,z", "-y,x-y,-z", "y,-x+y,z", "-x,-y,-z"]


hm_notation: P 42/n c m %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,z", "y,x,1/2-z", "y,-x,-z", "1/2-y,1/2+x,1/2+z", "x,-y,1/2+z", "1/2-x,1/2+y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,z", "-y,-x,1/2-z", "-y,x,-z", "1/2+y,1/2-x,1/2+z", "-x,y,1/2+z", "1/2+x,1/2-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 42 3 2
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "1/2-x,1/2+z,1/2+y", "1/2-z,1/2+y,1/2+x", "1/2-y,1/2+x,1/2+z", "1/2-x,1/2-z,1/2-y", "1/2-z,1/2-y,1/2-x", "1/2-y,1/2-x,1/2-z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "1/2+x,1/2-z,1/2+y", "1/2+z,1/2-y,1/2+x", "1/2+y,1/2-x,1/2+z", "1/2+x,1/2+z,1/2-y", "1/2+z,1/2+y,1/2-x", "1/2+y,1/2+x,1/2-z", "z,x,y", "y,z,x"]


hm_notation: P 4/n n c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "y,x,-z", "1/2+y,1/2-x,1/2-z", "-y,x,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "-y,-x,-z", "1/2-y,1/2+x,1/2-z", "y,-x,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I c m a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,z", "1/2-x,+y,1/2+z", "x,1/2-y,-z", "1/2+x,-y,1/2-z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "-x,1/2-y,z", "1/2-x,-y,1/2+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P m n m %var1%
symmetry_xyz:
["x,y,z", "-x,y,z", "1/2+x,-y,1/2-z", "x,y,-z", "1/2-x,-y,1/2+z", "1/2+x,-y,1/2+z", "-x,y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P c m b
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "-x,y,1/2+z", "x,-y,1/2-z", "x,1/2-y,z", "-x,1/2+y,-z", "-x,-y,-z"]


hm_notation: P m c n %var1%
symmetry_xyz:
["x,y,z", "-x,y,z", "1/2+x,1/2-y,-z", "1/2+x,1/2+y,1/2-z", "-x,-y,1/2+z", "x,-y,1/2+z", "1/2-x,1/2+y,1/2-z", "1/2-x,1/2-y,-z"]


hm_notation: I 2 m b %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2+y,-z", "1/2+x,+y,1/2-z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P m c n %var2%
symmetry_xyz:
["x,y,z", "-x,y,z", "1/2+x,-y,1/2-z", "1/2+x,1/2+y,-z", "-x,1/2-y,1/2+z", "x,1/2-y,1/2+z", "1/2-x,1/2+y,-z", "1/2-x,-y,1/2-z"]


hm_notation: I 1 2/a 1 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,-y,1/2-z", "-x,1/2-y,-z"]


hm_notation: A 1 1 2/m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "-x,-y,z", "-x,1/2-y,1/2+z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: C c c 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,-y,1/2+z", "1/2+x,1/2-y,1/2+z", "-x,y,1/2+z", "1/2-x,1/2+y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,z"]


hm_notation: I b m 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,z", "1/2-x,+y,1/2+z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: I m c b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,y,-z", "+x,1/2+y,1/2-z", "1/2-x,-y,z", "-x,1/2-y,1/2+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: I 1 2/m 1 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,1/2+y,-z", "1/2-x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: A 1 2/a 1 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,1/2-y,z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: P 42/n m c %var2%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "1/2+y,-x,1/2-z", "1/2-y,x,1/2+z", "x,1/2-y,z", "-x,1/2+y,-z", "1/2+x,1/2+y,-z", "1/2-x,1/2-y,z", "y,x,1/2+z", "-y,-x,1/2-z", "-y,1/2+x,1/2-z", "y,1/2-x,1/2+z", "1/2-x,y,z", "1/2+x,-y,-z", "-x,-y,-z"]


hm_notation: P n m b
symmetry_xyz:
["x,y,z", "-x,1/2+y,1/2+z", "x,1/2-y,1/2-z", "x,-y,z", "-x,y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "-x,-y,-z"]


hm_notation: P c n b
symmetry_xyz:
["x,y,z", "x,1/2+y,-z", "-x,1/2-y,z", "1/2-x,y,1/2+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z"]


hm_notation: P 6 2 2
symmetry_xyz:
["x,y,z", "x,x-y,-z", "x-y,x,z", "y,x,-z", "-y,x-y,z", "-x+y,y,-z", "-x,-y,z", "-x,-x+y,-z", "-x+y,-x,z", "-y,-x,-z", "y,-x+y,z", "x-y,-y,-z"]


hm_notation: P 4 21 2 %var1%
symmetry_xyz:
["x,y,z", "1/2+y,1/2+x,-z", "1/2-y,x,z", "-x,1/2+y,-z", "1/2-x,1/2-y,z", "-y,-x,-z", "y,1/2-x,z", "1/2+x,-y,-z"]


hm_notation: F d 3 c %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "3/4+z,3/4-x,3/4+y", "3/4+z,1/4-x,1/4+y", "1/4+z,3/4-x,1/4+y", "1/4+z,1/4-x,3/4+y", "1/2-y,1/2+z,-x", "1/2-y,+z,1/2-x", "-y,1/2+z,1/2-x", "-y,+z,-x", "1/4+x,1/4-y,3/4+z", "1/4+x,3/4-y,1/4+z", "3/4+x,1/4-y,1/4+z", "3/4+x,3/4-y,3/4+z", "1/2-z,x,1/2-y", "1/2-z,1/2+x,-y", "-z,x,-y", "-z,1/2+x,1/2-y", "3/4+y,1/4-z,1/4+x", "3/4+y,3/4-z,3/4+x", "1/4+y,1/4-z,3/4+x", "1/4+y,3/4-z,1/4+x", "-x,1/2+y,1/2-z", "-x,+y,-z", "1/2-x,1/2+y,-z", "1/2-x,+y,1/2-z", "1/2+x,-z,-y", "1/2+x,1/2-z,1/2-y", "+x,-z,1/2-y", "+x,1/2-z,-y", "3/4-z,1/4+y,3/4+x", "3/4-z,3/4+y,1/4+x", "1/4-z,1/4+y,1/4+x", "1/4-z,3/4+y,3/4+x", "y,1/2-x,-z", "y,-x,1/2-z", "1/2+y,1/2-x,1/2-z", "1/2+y,-x,-z", "1/4-x,1/4+z,1/4+y", "1/4-x,3/4+z,3/4+y", "3/4-x,1/4+z,3/4+y", "3/4-x,3/4+z,1/4+y", "z,-y,1/2-x", "z,1/2-y,-x", "1/2+z,-y,-x", "1/2+z,1/2-y,1/2-x", "3/4-y,3/4+x,1/4+z", "3/4-y,1/4+x,3/4+z", "1/4-y,3/4+x,3/4+z", "1/4-y,1/4+x,1/4+z", "x,1/2+z,y", "x,+z,1/2+y", "1/2+x,1/2+z,1/2+y", "1/2+x,+z,y", "1/4-z,1/4-y,1/4-x", "1/4-z,3/4-y,3/4-x", "3/4-z,1/4-y,3/4-x", "3/4-z,3/4-y,1/4-x", "1/2+y,x,z", "1/2+y,1/2+x,1/2+z", "+y,x,1/2+z", "+y,1/2+x,z", "3/4-x,1/4-z,3/4-y", "3/4-x,3/4-z,1/4-y", "1/4-x,1/4-z,1/4-y", "1/4-x,3/4-z,3/4-y", "1/2+z,1/2+y,1/2+x", "1/2+z,+y,+x", "+z,1/2+y,+x", "+z,+y,1/2+x", "1/4-y,3/4-x,3/4-z", "1/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,3/4-z", "3/4+z,1/4+x,1/4-y", "3/4+z,3/4+x,3/4-y", "1/4+z,1/4+x,3/4-y", "1/4+z,3/4+x,1/4-y", "1/2-y,1/2-z,x", "1/2-y,-z,1/2+x", "-y,1/2-z,1/2+x", "-y,-z,x", "1/4+x,3/4+y,1/4-z", "1/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,1/4-z", "1/2-z,-x,1/2+y", "1/2-z,1/2-x,+y", "-z,-x,+y", "-z,1/2-x,1/2+y", "3/4+y,3/4+z,3/4-x", "3/4+y,1/4+z,1/4-x", "1/4+y,3/4+z,1/4-x", "1/4+y,1/4+z,3/4-x", "-x,1/2-y,1/2+z", "-x,-y,+z", "1/2-x,1/2-y,+z", "1/2-x,-y,1/2+z", "1/4-z,3/4+x,1/4+y", "1/4-z,1/4+x,3/4+y", "3/4-z,3/4+x,3/4+y", "3/4-z,1/4+x,1/4+y", "1/2+y,-z,1/2-x", "1/2+y,1/2-z,-x", "+y,-z,-x", "+y,1/2-z,1/2-x", "3/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,3/4+z", "1/4-x,1/4+y,3/4+z", "1/4-x,3/4+y,1/4+z", "1/2+z,1/2-x,-y", "1/2+z,-x,1/2-y", "+z,1/2-x,1/2-y", "+z,-x,-y", "1/4-y,1/4+z,3/4+x", "1/4-y,3/4+z,1/4+x", "3/4-y,1/4+z,1/4+x", "3/4-y,3/4+z,3/4+x", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "1/2-x,1/2+z,1/2-y", "1/2-x,+z,-y", "-x,1/2+z,-y", "-x,+z,1/2-y", "1/4+z,1/4-y,1/4+x", "1/4+z,3/4-y,3/4+x", "3/4+z,1/4-y,3/4+x", "3/4+z,3/4-y,1/4+x", "-y,x,1/2-z", "-y,1/2+x,-z", "1/2-y,x,-z", "1/2-y,1/2+x,1/2-z", "3/4+x,1/4-z,3/4+y", "3/4+x,3/4-z,1/4+y", "1/4+x,1/4-z,1/4+y", "1/4+x,3/4-z,3/4+y", "-z,1/2+y,-x", "-z,+y,1/2-x", "1/2-z,1/2+y,1/2-x", "1/2-z,+y,-x", "1/4+y,3/4-x,3/4+z", "1/4+y,1/4-x,1/4+z", "3/4+y,3/4-x,1/4+z", "3/4+y,1/4-x,3/4+z", "-x,-z,1/2+y", "-x,1/2-z,+y", "1/2-x,-z,+y", "1/2-x,1/2-z,1/2+y", "3/4+z,1/4+y,3/4-x", "3/4+z,3/4+y,1/4-x", "1/4+z,1/4+y,1/4-x", "1/4+z,3/4+y,3/4-x", "1/2-y,1/2-x,1/2+z", "1/2-y,-x,+z", "-y,1/2-x,+z", "-y,-x,1/2+z", "1/4+x,1/4+z,1/4-y", "1/4+x,3/4+z,3/4-y", "3/4+x,1/4+z,3/4-y", "3/4+x,3/4+z,1/4-y", "1/2-z,-y,x", "1/2-z,1/2-y,1/2+x", "-z,-y,1/2+x", "-z,1/2-y,x", "3/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,3/4-z", "1/4+y,1/4+x,1/4-z", "1/4-z,1/4-x,3/4-y", "1/4-z,3/4-x,1/4-y", "3/4-z,1/4-x,1/4-y", "3/4-z,3/4-x,3/4-y", "1/2+y,z,1/2+x", "1/2+y,1/2+z,+x", "+y,z,+x", "+y,1/2+z,1/2+x", "3/4-x,3/4-y,3/4-z", "3/4-x,1/4-y,1/4-z", "1/4-x,3/4-y,1/4-z", "1/4-x,1/4-y,3/4-z", "1/2+z,1/2+x,y", "1/2+z,+x,1/2+y", "+z,1/2+x,1/2+y", "+z,+x,y", "1/4-y,3/4-z,1/4-x", "1/4-y,1/4-z,3/4-x", "3/4-y,3/4-z,3/4-x", "3/4-y,1/4-z,1/4-x"]


hm_notation: I b m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,y,1/2-z", "1/2+x,1/2+y,-z", "-x,-y,1/2+z", "1/2-x,1/2-y,+z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 4 n c
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "-y,x,z", "1/2+x,1/2-y,1/2+z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "y,-x,z", "1/2-x,1/2+y,1/2+z"]


hm_notation: F 2 m m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,z", "x,-y,-z", "x,1/2-y,1/2-z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z"]


hm_notation: C m c m %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,1/2+y,1/2-z", "1/2-x,y,z", "-x,1/2+y,z", "x,1/2-y,-z", "1/2+x,-y,-z", "x,y,1/2-z", "1/2+x,1/2+y,1/2-z", "1/2-x,1/2-y,1/2+z", "-x,-y,1/2+z", "1/2-x,1/2-y,-z", "-x,-y,-z"]


hm_notation: I 1 2/a 1 %var2%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,y,-z", "1/2-x,1/2+y,1/2-z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "1/2-x,1/2-y,-z", "-x,-y,1/2-z"]


hm_notation: I m a b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,y,-z", "+x,1/2+y,1/2-z", "1/2-x,-y,z", "-x,1/2-y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z", "-x,y,z", "1/2-x,1/2+y,1/2+z", "1/2-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "-x,-y,-z", "1/2-x,1/2-y,1/2-z"]


hm_notation: P 42/n b c %var1%
symmetry_xyz:
["x,y,z", "-y,-x,1/2+z", "1/2+y,1/2+x,1/2-z", "y,-x,1/2-z", "1/2-y,1/2+x,1/2+z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2+x,1/2+y,-z", "-x,-y,z", "y,x,1/2+z", "1/2-y,1/2-x,1/2-z", "-y,x,1/2-z", "1/2+y,1/2-x,1/2+z", "1/2-x,1/2+y,z", "x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: F 1 2/d 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "3/4-x,y,3/4-z", "3/4-x,1/2+y,1/4-z", "1/4-x,y,1/4-z", "1/4-x,1/2+y,3/4-z", "1/2-x,-y,1/2-z", "1/2-x,1/2-y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: P 64 2 2
symmetry_xyz:
["x,y,z", "x,x-y,2/3-z", "x-y,x,2/3+z", "y,x,1/3-z", "-y,x-y,1/3+z", "-x+y,y,-z", "-x,-y,z", "-x,-x+y,2/3-z", "-x+y,-x,2/3+z", "-y,-x,1/3-z", "y,-x+y,1/3+z", "x-y,-y,-z"]


hm_notation: C 1 1 2/a
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "1/2+x,y,-z", "+x,1/2+y,-z", "1/2-x,-y,z", "-x,1/2-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: A 21 2 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2-x,-y,z", "1/2-x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P 65 2 2
symmetry_xyz:
["x,y,z", "x,x-y,5/6-z", "x-y,x,5/6+z", "y,x,2/3-z", "-y,x-y,2/3+z", "-x+y,y,1/2-z", "-x,-y,1/2+z", "-x,-x+y,1/3-z", "-x+y,-x,1/3+z", "-y,-x,1/6-z", "y,-x+y,1/6+z", "x-y,-y,-z"]


hm_notation: F 1 d 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z"]


hm_notation: F 1 2/d 1 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,-y,1/4+z", "1/4+x,1/2-y,3/4+z", "3/4+x,-y,3/4+z", "3/4+x,1/2-y,1/4+z", "3/4-x,y,1/4-z", "3/4-x,1/2+y,3/4-z", "1/4-x,y,3/4-z", "1/4-x,1/2+y,1/4-z", "1/2-x,-y,-z", "1/2-x,1/2-y,1/2-z", "-x,-y,1/2-z", "-x,1/2-y,-z"]


hm_notation: A 1 2/n 1
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2-x,y,1/2-z", "1/2-x,1/2+y,-z", "1/2+x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: F 2 d d
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,1/4+y,1/4-z", "1/4+x,3/4+y,3/4-z", "3/4+x,1/4+y,3/4-z", "3/4+x,3/4+y,1/4-z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "+x,-y,-z", "+x,1/2-y,1/2-z"]


hm_notation: B b c m
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "1/2-x,1/2+y,z", "-x,1/2+y,1/2+z", "1/2+x,1/2-y,-z", "+x,1/2-y,1/2-z", "x,y,-z", "1/2+x,y,1/2-z", "-x,-y,z", "1/2-x,-y,1/2+z", "1/2+x,1/2-y,z", "+x,1/2-y,1/2+z", "1/2-x,1/2+y,-z", "-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P b n b
symmetry_xyz:
["x,y,z", "1/2-x,1/2+y,z", "1/2+x,1/2-y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "1/2-x,y,1/2-z", "-x,-y,-z"]


hm_notation: C m m b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "-x,1/2+y,z", "1/2-x,+y,z", "x,1/2-y,-z", "1/2+x,-y,-z", "x,-y,z", "1/2+x,1/2-y,z", "-x,y,-z", "1/2-x,1/2+y,-z", "x,1/2+y,-z", "1/2+x,+y,-z", "-x,1/2-y,z", "1/2-x,-y,z", "-x,-y,-z", "1/2-x,1/2-y,-z"]


hm_notation: A b m a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2-z", "1/2+x,1/2+y,-z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,+z", "x,-y,z", "x,1/2-y,1/2+z", "-x,y,-z", "-x,1/2+y,1/2-z", "1/2-x,y,1/2+z", "1/2-x,1/2+y,+z", "1/2+x,-y,1/2-z", "1/2+x,1/2-y,-z", "-x,-y,-z", "-x,1/2-y,1/2-z"]


hm_notation: I b a 2
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,-y,1/2+z", "1/2+x,1/2-y,+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: A 21 a m
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,-y,z", "1/2+x,1/2-y,1/2+z", "x,y,-z", "x,1/2+y,1/2-z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: P n a b
symmetry_xyz:
["x,y,z", "1/2+x,-y,z", "1/2-x,y,-z", "x,1/2+y,1/2-z", "-x,1/2-y,1/2+z", "1/2-x,1/2+y,1/2+z", "1/2+x,1/2-y,1/2-z", "-x,-y,-z"]


hm_notation: A 21 m a
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,-z", "1/2+x,1/2+y,1/2-z", "x,-y,z", "x,1/2-y,1/2+z", "1/2+x,-y,-z", "1/2+x,1/2-y,1/2-z"]


hm_notation: F 1 d 1 %var1%
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+x,1/4-y,1/4+z", "1/4+x,3/4-y,3/4+z", "3/4+x,1/4-y,3/4+z", "3/4+x,3/4-y,1/4+z"]


hm_notation: B 1 21/m 1
symmetry_xyz:
["x,y,z", "1/2+x,y,1/2+z", "x,1/2-y,z", "1/2+x,1/2-y,1/2+z", "-x,1/2+y,-z", "1/2-x,1/2+y,1/2-z", "-x,-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: P b a a
symmetry_xyz:
["x,y,z", "1/2+x,y,-z", "1/2-x,-y,z", "1/2+x,1/2-y,z", "1/2-x,1/2+y,-z", "-x,1/2+y,z", "x,1/2-y,-z", "-x,-y,-z"]


hm_notation: P 21 3 %var1%
symmetry_xyz:
["x,y,z", "-z,1/2-x,1/2+y", "1/2-z,1/2+x,-y", "1/2+z,-x,1/2-y", "z,x,y", "1/2+y,-z,1/2-x", "-y,1/2-z,1/2+x", "1/2-y,1/2+z,-x", "y,z,x", "1/2-x,1/2+y,-z", "1/2+x,-y,1/2-z", "-x,1/2-y,1/2+z"]


hm_notation: I m a 2 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "1/2+x,-y,z", "+x,1/2-y,1/2+z", "1/2-x,y,z", "-x,1/2+y,1/2+z", "-x,-y,z", "1/2-x,1/2-y,1/2+z"]


hm_notation: I 21 21 21 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-x,1/2+y,1/2-z", "1/2-x,+y,-z", "1/2+x,1/2-y,-z", "+x,-y,1/2-z", "1/2-x,-y,1/2+z", "-x,1/2-y,+z"]


hm_notation: P 62 2 2 %var1%
symmetry_xyz:
["x,y,z", "x,x-y,-z", "x-y,x,1/3+z", "y,x,1/3-z", "-y,x-y,2/3+z", "-x+y,y,2/3-z", "-x,-y,z", "-x,-x+y,-z", "-x+y,-x,1/3+z", "-y,-x,1/3-z", "y,-x+y,2/3+z", "x-y,-y,2/3-z"]


hm_notation: F -4 d 2
symmetry_xyz:
["x,y,z", "x,1/2+y,1/2+z", "1/2+x,y,1/2+z", "1/2+x,1/2+y,z", "1/4+y,1/4+x,3/4-z", "1/4+y,3/4+x,1/4-z", "3/4+y,1/4+x,1/4-z", "3/4+y,3/4+x,3/4-z", "1/4-x,1/4+y,3/4+z", "1/4-x,3/4+y,1/4+z", "3/4-x,1/4+y,1/4+z", "3/4-x,3/4+y,3/4+z", "1/4-y,1/4-x,3/4-z", "1/4-y,3/4-x,1/4-z", "3/4-y,1/4-x,1/4-z", "3/4-y,3/4-x,3/4-z", "1/4+x,1/4-y,3/4+z", "1/4+x,3/4-y,1/4+z", "3/4+x,1/4-y,1/4+z", "3/4+x,3/4-y,3/4+z", "1/2+y,-x,1/2-z", "1/2+y,1/2-x,-z", "+y,-x,-z", "+y,1/2-x,1/2-z", "1/2-x,-y,1/2+z", "1/2-x,1/2-y,+z", "-x,-y,+z", "-x,1/2-y,1/2+z", "1/2-y,x,1/2-z", "1/2-y,1/2+x,-z", "-y,x,-z", "-y,1/2+x,1/2-z"]


hm_notation: P 42/m m c %var1%
symmetry_xyz:
["x,y,z", "1/2-y,1/2-x,1/2+z", "1/2+y,1/2+x,1/2-z", "1/2+y,1/2-x,1/2-z", "1/2-y,1/2+x,1/2+z", "x,-y,z", "-x,y,-z", "x,y,-z", "-x,-y,z", "1/2+y,1/2+x,1/2+z", "1/2-y,1/2-x,1/2-z", "1/2-y,1/2+x,1/2-z", "1/2+y,1/2-x,1/2+z", "-x,y,z", "x,-y,-z", "-x,-y,-z"]


hm_notation: I 1 2/c 1 %var1%
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,1/2-y,1/2+z", "1/2+x,-y,+z", "-x,y,1/2-z", "1/2-x,1/2+y,-z", "-x,1/2-y,-z", "1/2-x,-y,1/2-z"]


hm_notation: I 41 c d
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "-y,1/2-x,3/4+z", "1/2-y,-x,1/4+z", "-y,1/2+x,1/4+z", "1/2-y,+x,3/4+z", "1/2+x,1/2-y,z", "+x,-y,1/2+z", "1/2-x,1/2-y,1/2+z", "-x,-y,+z", "1/2+y,x,1/4+z", "+y,1/2+x,3/4+z", "1/2+y,-x,3/4+z", "+y,1/2-x,1/4+z", "-x,y,1/2+z", "1/2-x,1/2+y,+z"]


hm_notation: P 4 3 2
symmetry_xyz:
["x,y,z", "-z,x,-y", "-y,z,-x", "-x,y,-z", "-x,z,y", "-z,y,x", "-y,x,z", "-x,-z,-y", "-z,-y,-x", "-y,-x,-z", "-z,-x,y", "-y,-z,x", "-x,-y,z", "z,-x,-y", "y,-z,-x", "x,-y,-z", "x,-z,y", "z,-y,x", "y,-x,z", "x,z,-y", "z,y,-x", "y,x,-z", "z,x,y", "y,z,x"]


hm_notation: C 2 c b
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,z", "x,1/2-y,1/2+z", "1/2+x,-y,1/2+z", "x,1/2+y,1/2-z", "1/2+x,+y,1/2-z", "x,-y,-z", "1/2+x,1/2-y,-z"]


hm_notation: I 2 m m
symmetry_xyz:
["x,y,z", "1/2+x,1/2+y,1/2+z", "x,y,-z", "1/2+x,1/2+y,1/2-z", "x,-y,z", "1/2+x,1/2-y,1/2+z", "x,-y,-z", "1/2+x,1/2-y,1/2-z"]


# cif

formula: Pb S
compound: Colorado, USA
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 5.93
b: 5.93
c: 5.93
alpha: 90
beta: 90
gamma: 90
cell_volume: 208.528
crystal_density: 7.621
atoms_sites: ["Pb", "S"]
atoms_x: AAAAAICEHgA=
atoms_y: AAAAAICEHgA=
atoms_z: AAAAAICEHgA=
atoms_occupancy: 0
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atoms_aniso_label: "<missing>"
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qdat:
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formula: Pb Se
compound: Synthetic
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 6.14
b: 6.14
c: 6.14
alpha: 90
beta: 90
gamma: 90
cell_volume: 231.476
crystal_density: 8.211
atoms_sites: ["Pb", "Se"]
atoms_x: AAAAAICEHgA=
atoms_y: AAAAAICEHgA=
atoms_z: AAAAAICEHgA=
atoms_occupancy: 0
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qdat:
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formula: Pb Te
compound: Synthetic
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 6.34
b: 6.34
c: 6.34
alpha: 90
beta: 90
gamma: 90
cell_volume: 254.840
crystal_density: 8.726
atoms_sites: ["Pb", "Te"]
atoms_x: AAAAAICEHgA=
atoms_y: AAAAAICEHgA=
atoms_z: AAAAAICEHgA=
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
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qdat:
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formula: Fe S2
compound: natural, unknown
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 5.38
b: 5.38
c: 5.38
alpha: 90
beta: 90
gamma: 90
cell_volume: 155.721
crystal_density: 5.118
atoms_sites: ["Fe", "S"]
atoms_x: AAAAAEChFAA=
atoms_y: AAAAAEChFAA=
atoms_z: AAAAAEChFAA=
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
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qdat:
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formula: Hg S
compound: unknown
pub_title: The crystal structures of some metallic sulfides
formula_title: <missing>
a: 4.15
b: 4.15
c: 9.51
alpha: 90
beta: 90
gamma: 120
cell_volume: 141.843
crystal_density: 8.171
atoms_sites: ["Hg", "S"]
atoms_x: VVgUAFVYFAA=
atoms_y: VVgUAFVYFAA=
atoms_z: AAAAAICEHgA=
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
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qdat:
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formula: Fe S2
compound: Joplin, Missouri, USA
pub_title: The crystal structure of marcasite
formula_title: <missing>
a: 3.37
b: 4.44
c: 5.39
alpha: 90
beta: 90
gamma: 90
cell_volume: 80.649
crystal_density: 4.941
atoms_sites: ["Fe", "S"]
atoms_x: AAAAAAAAAAA=
atoms_y: AAAAAOBjDAA=
atoms_z: AAAAAGDjFgA=
atoms_occupancy: 0
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qdat:
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formula: S K O3
compound: <missing>
formula_title: K2S2O6
a: 9.82
b: 9.82
c: 6.36
alpha: 90
beta: 90
gamma: 120
cell_volume: 531.142
crystal_density: 2.235
atoms_sites: ["S1", "S2", "S3", "K1", "K2", "O1", "O2", "O3"]
atoms_x: AAAAAFVYFABVWBQAYOMWAEAdKgAgEgoAYIklAKDSHgA=
atoms_y: AAAAAKuwKACrsCgAYOMWAEAdKgDAtgYAQGAKAEDRDAA=
atoms_z: AMQJAMACJADAehAAAAAAAICEHgDACQ4AgMAUAADUMAA=
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
atoms_aniso_u11: 0
atoms_aniso_u22: 0
atoms_aniso_u33: 0
atoms_aniso_u12: 0
atoms_aniso_u13: 0
atoms_aniso_u23: 0
pub_title:
 The crystal structure of potassium dithionate, K2S2O6
 Note: coordinates revised according to Am Min 18 (1933) 455-457

qdat:
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formula: S Rb O3
compound: <missing>
pub_title: The crystal structure of potassium dithionate, K2S2O6
formula_title: Rb2S2O6
a: 10.0
b: 10.0
c: 6.3
alpha: 90
beta: 90
gamma: 120
cell_volume: 545.596
crystal_density: 3.023
atoms_sites: ["S1", "S2", "S3", "Rb1", "Rb2", "O1", "O2", "O3"]
atoms_x: AAAAAFVYFABVWBQAgE8SAKAlJgAgEgoAYIklAKDSHgA=
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qdat:
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formula: Cu.53 Fe.31 Zn.01 Sn.05 Mo.09 S.71 As.03 Te.02 Sb.01
compound: Leonard mine, Butte, Montana, USA
pub_title: X-Ray examination of colusite, (Cu,Fe,Mo,Sn)4(S,As,Te)3-4
formula_title: <missing>
a: 5.304
b: 5.304
c: 5.304
alpha: 90
beta: 90
gamma: 90
cell_volume: 149.214
crystal_density: 4.229
atoms_sites: ["Cu", "Fe", "Zn", "Sn", "Mo", "S", "As", "Te", "Sb"]
atoms_x: AAAAAAAAAAAAAAAAAAAAAAAAAABAQg8AQEIPAEBCDwBAQg8A
atoms_y: AAAAAAAAAAAAAAAAAAAAAAAAAABAQg8AQEIPAEBCDwBAQg8A
atoms_z: AAAAAAAAAAAAAAAAAAAAAAAAAABAQg8AQEIPAEBCDwBAQg8A
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qdat:
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formula: Sb Na Be4 O7
compound: not given
pub_title: The crystal structure of swedenborgite, NaBe4SbO7
formula_title: <missing>
a: 5.47
b: 5.47
c: 8.92
alpha: 90
beta: 90
gamma: 120
cell_volume: 231.137
crystal_density: 4.207
atoms_sites: ["Sb", "Na", "Be1", "Be2", "O1", "O2", "O3"]
atoms_x: VVgUAFVYFAAAAAAAOCwKAAAAAACAhB4AOCwKAA==
atoms_y: q7AoAKuwKAAAAAAAyNP1/wAAAACAe+H/yNP1/w==
atoms_z: AAAAAKAlJgCQ0AMA0BITAGDjFgBg4xYAIKEHAA==
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qdat:
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formula: Fe Sb2 S4
compound: <missing>
pub_title: The crystal structure of berthierite
formula_title: <missing>
a: 11.44
b: 14.12
c: 3.76
alpha: 90
beta: 90
gamma: 90
cell_volume: 607.363
crystal_density: 4.676
atoms_sites: ["Fe", "Sb1", "Sb2", "S1", "S2", "S3", "S4"]
atoms_x: kNADALBxCwCwcQsAkNADALBxCwCwcQsAkNADAA==
atoms_y: QEIPAOBnNQCgJSYAAAAAACChBwBg4xYAwMYtAA==
atoms_z: QEIPAEBCDwBAQg8AQEIPAEBCDwBAQg8AQEIPAA==
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
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qdat:
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formula: Sb2 O3
compound: <missing>
pub_title: The crystal structure of valentinite
formula_title: <missing>
a: 4.92
b: 12.46
c: 5.42
alpha: 90
beta: 90
gamma: 90
cell_volume: 332.263
crystal_density: 5.827
atoms_sites: ["Sb", "O1", "O2"]
atoms_x: cGoHAEBCDwBASfn/
atoms_y: YKIMAEBCDwCAhQkA
atoms_z: YK4KACBs+/9grgoA
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
atoms_aniso_u11: 0
atoms_aniso_u22: 0
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qdat:
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formula: K S2 Al3 O14 H6
compound: <missing>
pub_title: The crystal structures of alunite and the jarosites
formula_title: <missing>
a: 6.96
b: 6.96
c: 17.35
alpha: 90
beta: 90
gamma: 120
cell_volume: 727.861
crystal_density: 2.835
atoms_sites: ["K", "S", "Al", "O1", "O2", "O-H3"]
atoms_x: AAAAAAAAAAAAAAAAAAAAAGAfDQDAJwkA
atoms_y: AAAAAAAAAACAhB4AAAAAAKDg8v9A2Pb/
atoms_z: AAAAAKCdEgCAhB4AoPwXAMB1/P/AsAcA
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
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qdat:
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formula: Al2 Ca3 Si2.001 O12
compound: <missing>
pub_title: The crystal structure of plazolite
formula_title: <missing>
a: 12.140
b: 12.140
c: 12.140
alpha: 90
beta: 90
gamma: 90
cell_volume: 1789.188
crystal_density: 3.136
atoms_sites: ["Al", "Ca", "Si", "O"]
atoms_x: AAAAAEBCDwBAQg8A4CICAA==
atoms_y: AAAAACChBwBg4xYAAHECAA==
atoms_z: AAAAAAAAAAAAAAAAQKwnAA==
atoms_occupancy: AAk9AAAJPQDgtSgAAAk9AA==
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qdat:
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formula: Cu Fe O2
compound: <missing>
pub_title: Crystal structure and density of delafossite
formula_title: <missing>
a: 5.96
b: 5.96
c: 5.96
alpha: 29.43
beta: 29.43
gamma: 29.43
cell_volume: 45.238
crystal_density: 5.557
atoms_sites: ["Cu", "Fe", "O"]
atoms_x: AAAAAICEHgAYyAYA
atoms_y: AAAAAICEHgAYyAYA
atoms_z: AAAAAICEHgAYyAYA
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
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qdat:
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formula: Fe Sb S
compound: <missing>
pub_title: The crystal structure of gudmundite
formula_title: <missing>
a: 6.02
b: 5.93
c: 6.02
alpha: 90
beta: 67.87
gamma: 90
cell_volume: 199.074
crystal_density: 6.995
atoms_sites: ["Fe", "Sb", "S"]
atoms_x: gLDt/yAYCQCARer/
atoms_y: YOoAAOD+BwCg2QgA
atoms_z: gE8SAIAOCADgtSgA
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atoms_aniso_label: "<missing>"
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qdat:
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formula: Fe Sb S
compound: <missing>
pub_title: The crystal structure of gudmundite
formula_title: <missing>
a: 10.00
b: 5.93
c: 6.73
alpha: 90
beta: 90.
gamma: 90
cell_volume: 399.089
crystal_density: 6.979
atoms_sites: ["Fe", "Sb", "S"]
atoms_x: AAAAAICLCACAhQkA
atoms_y: YOoAAOD+BwCg2QgA
atoms_z: gE8SAACD//9gMB8A
atoms_occupancy: 0
atoms_u_iso: 0
atoms_aniso_label: "<missing>"
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formula: Si.5 Fe1.4 O4.001 H1.667
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formula_title: <missing>
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pub_title:
 Random structures of layer minerals as illustrated by cronstedtite
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formula: Na.35 (Al1.624 Mg.376) F3.882 O2.993 H2.993
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formula: Au Ag Te4
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formula: Ba Fe Si4 O10
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formula: Ni Te2
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pub_title: On melonite from Quebec and the crystal structure of NiTe2
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compound: <missing>
pub_title: Some computations on svanbergite, woodhouseite and alunite trial C
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formula: Fe2 Cu S3
compound: <missing>
pub_title: The crystal structure of cubanite
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formula: Cu1.4 Te
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formula: Cu1.25 Fe.25 S
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pub_title: On the symmetry and crystal structure of bornite
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formula: C
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formula: Hg Se
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formula: Pb2 Ni3 S2
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formula: As2 O3
compound: <missing>
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formula: Bi V O4
compound: <missing>
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formula: Au Sb2
compound: Giant Yellowknife mine, Northwest Territories, Canada
pub_title: Aurostibite, AuSb2; A new mineral in the pyrite group
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formula: Bi V O4
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formula: (Ca1.7 Na.2 K.1) Si2 Mg.5 Al.4 O7
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formula: Ce C O3 F
compound: <missing>
pub_title: The crystallography of bastnaesite, parasite, roentgenite, and synchisite
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formula: (Fe.125 V.875) (O2 H)
compound: <missing>
pub_title: The crystal structure of montroseite, a vanadium member of the diaspore group
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b: 9.97
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formula: Cu S
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formula: Cu Se
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formula: Fe2 Cu S3
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formula: Cd S
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formula: Pb Mn V O7 H
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pub_title: The structures of the minerals of the descloizite and adelite groups: II - pyrobelonite.
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formula: Pb Cu5.999 O8
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pub_title: The crystal structure of murdochite disordered model
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formula: K Mg3 (Si3 Al) O12 H2
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formula: (Ni4.5 Fe4.5) S8
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pub_title: Confirmation of the crystal structure of pentlandite.
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formula: Fe3 S4
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pub_title: Smythite, a new iron sulfide, and associated pyrrhotite from Indiana
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formula: U Si O4
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formula: Ba Si2 O5
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formula: Ca Mg C2 O6
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formula: Ag3 Au Te2
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formula: Zn S
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pub_title: New wurtzite polytypes from Joplin, Missouri
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formula: Ni.689 Fe.283 Co.027
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formula: Ni.689 Fe.283 Co.027
compound: Awarua Bay, New Zealand
pub_title: An association of awaruite with heazlewoodite
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formula: Ni.695 Fe.262 Co.039 Cu.003
compound: Eastern Townships, Quebec, USA
pub_title: An association of awaruite with heazlewoodite
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formula: V2 O5
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formula: V3 O8
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formula: As B Ca2 O8 H4
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formula: Ca C O3
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formula: Mn C O3
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formula: Fe C O3
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formula: Zn C O3
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pub_title: Crystallographic tables for the rhombohedral carbonates
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formula: Cd C O3
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pub_title: Crystallographic tables for the rhombohedral carbonates
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formula: Co C O3
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formula: Ni C O3
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formula: (Ca.5 Mn.5) C O3
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formula: Cu C O3
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formula: Ca Mg C2 O6
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formula: Cd Mg C2 O6
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formula: Zn S
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formula: Cd S
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formula: Fe As S
compound: <missing>
pub_title: Arsenopyrite crystal-chemical relations From Freiberg, Germany
formula_title: <missing>
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b: 5.675
c: 5.785
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formula: Ti Na2 Si4 O11
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pub_title: The determination and refinement of the structure of narsarsukite, Na2TiOSi4O10
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formula: Zn S
compound: Thomaston Dam, Connecticut
pub_title: Hydrothermal wurtzite at Thomaston Dam, Connecticut
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formula: Ca O2 H2
compound: <missing>
pub_title: A nuclear magnetic resonance determination of the hydrogen positions in Ca(OH)2 T = -190 C
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formula: Ca O2 H2
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pub_title: A nuclear magnetic resonance determination of the hydrogen positions in Ca(OH)2 T = 25 C
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formula: Cs (Fe Si2) O6
compound: <missing>
pub_title: A hydrothermally synthesized iron analog of pollucite - Its structure and significance
formula_title: CsFeSi2O6
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formula: Cu1.8 S
compound: <missing>
pub_title: Polymorphism in digenite high-temperature form at T = 80 C
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formula: Al2 Be O4
compound: <missing>
pub_title: Refinement of the chrysoberyl structure
formula_title: <missing>
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formula: (Ta.438 Fe.177 Sn.128 Nb.124 Mn.12 Zr.006 Ti.006 W.001) O2
compound: <missing>
formula_title: <missing>
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b: 4.742
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pub_title:
 Ixiolite - a columbite substructure
 sample M-6591, note that the coordinates have been put into a standard setting

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formula: Fe3 S4
compound: <missing>
pub_title: Greigite, the thio-spinel of iron; a new mineral
formula_title: <missing>
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formula: (K U) As O9 H6
compound: Fuemrol No. 2 mine, Temple Mountain, Emery County, Utah, USA
formula_title: <missing>
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pub_title:
 Studies of the torbernite minerals (I): The crystal structure of abernathyite
 and the structurally related compounds NH4(UO2AsO4).3H2O and K(H3O)(UO2AsO4)2.6H2O

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formula: N H10 U As O9
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pub_title:
 Studies of the torbernite minerals (I): The crystal structure of abernathyite
 and the structurally related compounds NH4(UO2AsO4).3H2O and K(H3O)(UO2AsO4)2.6H2O
 Sample : Abernathyite - NH4

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pub_title:
 Studies of the torbernite minerals (I): The crystal structure of abernathyite
 and the structurally related compounds NH4(UO2AsO4).3H2O and K(H3O)(UO2AsO4)2.6H2O
 Sample: Abernathyite - K(H3O)

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formula: Cs U V O6
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formula_title: <missing>
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beta: 106.08
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pub_title:
 The crystal structures of synthetic anhydrous carnotite, K2(UO2)2V2O8, and
 its cesium analogue, Cs2(UO2)2V2O8

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formula: Co As S
compound: <missing>
formula_title: <missing>
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b: 5.582
c: 5.582
alpha: 90
beta: 90
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pub_title:
 The crystal structures of ordered and disordered cobaltite
 ordered, annealed after heating in a vacuum at 450 C

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formula: Co (As S)
compound: <missing>
formula_title: <missing>
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b: 5.582
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pub_title:
 The crystal structures of ordered and disordered cobaltite
 disordered, annealed after heating in a vacuum to 850 C

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formula: Al2 Mg3 Si3 O12
compound: <missing>
formula_title: <missing>
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b: 11.459
c: 11.459
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beta: 90
gamma: 90
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pub_title:
 Refinement of the crystal structure of synthetic pyrope
 refinement D, note that temperature factors reported for Si were labelled
 incorrectly in the paper

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formula: Fe2 O3
compound: Elba, Italy
pub_title: Refinement of the hematite structure
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beta: 90
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formula: Fe P (O6 H4)
compound: <missing>
pub_title: The crystal structure of metastrengite and its relationship to strengite and phosphophyllite
formula_title: <missing>
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b: 9.77
c: 8.73
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gamma: 90
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formula: Cu3 V S4
compound: <missing>
formula_title: <missing>
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b: 5.3912
c: 5.3912
alpha: 90
beta: 90
gamma: 90
cell_volume: 156.695
crystal_density: 3.919
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pub_title:
 Refinement of the structure of sulvanite
 Note: symmetry constraints on B(i,j) reported incorrectly

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formula: Na Al Si2 O6
compound: <missing>
pub_title: The crystal structure of jadeite, NaAlSi2O6
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formula: Ca Mn Si2 O6
compound: <missing>
pub_title: Refinement of the crystal structure of johannsenite
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pub_title: Refinement of the crystal structure of a glauberite
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formula: (Cs.7 Na.3) (Al.99 Si2.01) O6
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pub_title: Crystal structure and optical properties of pollucite
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formula_title: <missing>
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pub_title:
 Crystal chemistry of the basic manganese arsenate minerals 1. The crystal
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formula: Y As Mn2 O8 H4
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formula_title: <missing>
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pub_title:
 Crystal chemistry of the basic manganese arsenate minerals 1. The crystal
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formula: Ba S O4
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pub_title: A refinement of the structure of barite from Cow Green mine
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formula: Ni (As1.23 S.77)
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pub_title: The crystal structure of disordered gersdorffite
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formula: (Mg1.8 Fe.2) Si O4
compound: <missing>
pub_title: Crystal structures of natural olivines
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compound: <missing>
pub_title: The crystal structure of augelite
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formula: Mn (Fe.5 Sb.5) O3
compound: <missing>
pub_title: Substitutions of the type (Sb0.5Fe0.5)-(Ti): The crystal structure of melanostibite
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formula_title: <missing>
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pub_title:
 Crystal chemistry of the basic manganese arsenates: III. The crystal structure
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formula: (Mg.8 Fe.2) O2.6 Cl.2 H2.6
compound: <missing>
pub_title: About the structure of iowaite
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formula: Mg3 Si O4.2 (F1.8 H.2)
compound: <missing>
pub_title: The crystal structures of the humite minerals: I. Norbergite
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formula: Ca Nb2 O6
compound: Synthetic
pub_title: The crystal structure of calcium niobate (CaNb2O6)
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formula: Sn Ta2 O7
compound: <missing>
pub_title: The crystal structure of SnTa2O7, thoreaulite, an example of tin in five-fold coordination
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formula: Pb2 Cr O5
compound: <missing>
pub_title: A study of phoenicochroite - its structure and properties
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formula: Fe3 P2 (O11 H3)
compound: <missing>
pub_title: The Fe3(H2O)n(PO4)2 homologous series: Crystal-chemical relationships and oxidized equivalents
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formula: Na3 Al2 Li3 F12
compound: <missing>
pub_title: Refinement of the crystal structure of cryolithionite, {Na3}[Al2](Li3)F12
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formula: W Fe O4
compound: <missing>
pub_title: The relation between "light wolframite" and common wolframite sample: light wolframite
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formula: W Fe O4
compound: <missing>
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formula: Fe S O7 H3
compound: <missing>
pub_title: The crystal structure of butlerite
formula_title: <missing>
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formula: Ca C O3
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pub_title: Crystal structures of aragonite, strontianite, and witherite
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formula: Sr C O3
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formula: Ca C O3
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pub_title: Refinement of the crystal structure of aragonite
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formula: Zr Si O4
compound: <missing>
pub_title: The structure of zircon: A comparison with garnet
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formula: Si3 (Al1.34 Cr.66) (Mg2.64 Fe.36) O12
compound: inclusioin in a Venezuelan diamond
pub_title: The crystal chemistry of the silicate garnets sample Cr-Py
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formula: Si3 Al2 Fe2.58 Mg.27 Ca.12 O12
compound: Emerald creek in Latah Co, Idaho, USA
pub_title: The crystal chemistry of the silicate garnets sample Al
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compound: Minas Gerais, Brazil
pub_title: The crystal chemistry of the silicate garnets sample Sp
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compound: unknown
pub_title: The crystal chemistry of the silicate garnets sample Mn-Gr
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compound: Asbestos, Quebec, Canada
pub_title: The crystal chemistry of the silicate garnets sample Gr
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formula: Si3 (Cr1.73 Al.21 Fe.05 Ti.01) (Ca2.991 Mn.009) O12
compound: Washington, Nevada Co, California, USA
pub_title: The crystal chemistry of the silicate garnets sample Uv
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formula: Si3 (V1.2 Al.48 Fe.32) (Ca2.91 Mg.09) O12
compound: Laguna Uranium mining district, New Mexico, USA
pub_title: The crystal chemistry of the silicate garnets sample Go
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formula: Si3 Fe2 Ca3 O12
compound: Valmalen, Italy
pub_title: The crystal chemistry of the silicate garnets sample An
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b: 12.058
c: 12.058
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formula: (K.84 Na.16) Ca4 Si8 O28 F H16
compound: Phoenix mine, Keweenaw Peninsula, Michigan, USA
pub_title: Refinement of the crystal structure of apophyllite I. X-ray diffraction and physical properties
formula_title: <missing>
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formula: Ag2 Se
compound: <missing>
pub_title: The crystal structure of the low-temperature form of silver selenide
formula_title: <missing>
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formula: Fe K S2 O8
compound: <missing>
pub_title: The crystal structures of yavapaiite, KFe(SO4)2, and goldichite, KFe(SO4)2.4H2O
formula_title: <missing>
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formula: Ni As2
compound: <missing>
pub_title: The crystal structure of pararammelsbergite (NiAs2)
formula_title: <missing>
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formula: (Fe.65 Mn.35) P O4
compound: Fletcher Quarry, North Groton, New Hampshire, USA
pub_title: The crystal structure of heterosite
formula_title: <missing>
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formula: Mn2 Ge O4
compound: <missing>
pub_title: Crystal structures of the high pressure polymorphs of Mn2GeO4
formula_title: Mn2GeO4-beta
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formula: Mn2 Ge O4
compound: <missing>
pub_title: Crystal structures of the high pressure polymorphs of Mn2GeO4
formula_title: Mn2GeO4-delta
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formula: Si Mg2 O4
compound: hypothetical
formula_title: <missing>
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b: 10.19
c: 5.85
alpha: 90
beta: 90
gamma: 90
cell_volume: 285.539
crystal_density: 3.273
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density

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formula: Si Mg2 O4
compound: hypothetical
formula_title: <missing>
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beta: 90
gamma: 90
cell_volume: 544.213
crystal_density: 3.434
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 Polymorphs of low and high density

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formula: Si Mg2 O4
compound: hypothetical
formula_title: <missing>
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gamma: 90
cell_volume: 535.387
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 normal

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formula: Si Mg2 O4
compound: hypothetical
formula_title: <missing>
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gamma: 90
cell_volume: 545.339
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 inverse

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formula: Si Mg2 O4
compound: hypothetical
formula_title: Mg2SiO4
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gamma: 90
cell_volume: 281.425
crystal_density: 3.321
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 Model II

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formula: Si Mg2 O4
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formula_title: Mg2SiO4
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crystal_density: 3.572
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 Model III

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formula: Si Mg2 O4
compound: hypothetical
formula_title: Mg2SiO4
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gamma: 90
cell_volume: 121.201
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 Sr2PbO4 structure

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formula: Si Mg2 O4
compound: hypothetical
formula_title: Mg2SiO4
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b: 3.51
c: 10.45
alpha: 90
beta: 90
gamma: 90
cell_volume: 128.745
crystal_density: 3.629
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pub_title:
 Computer-simulated crystal structures of observed and hypothetical Mg2SiO4
 polymorphs of low and high density
 K2MgF4 structure

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formula: Al Si2 O6 H
compound: <missing>
pub_title: The crystal structures of pyrophyllite, 1Tc, and of its dehydroxylate
formula_title: <missing>
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formula: Al2 Si4 O11
compound: <missing>
formula_title: <missing>
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alpha: 91.17
beta: 100.21
gamma: 88.62
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pub_title:
 The crystal structures of pyrophyllite, 1Tc, and of its dehydroxylate
 Note: this is polytype pyrophyllite-1Tc

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formula: Fe K S2 O8
compound: <missing>
pub_title: The crystal structure of yavapaiite: A discussion
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formula: As Ca Mg O4 F
compound: <missing>
pub_title: The crystal structure of tilasite
formula_title: <missing>
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formula: Na3 S O4 F
compound: <missing>
pub_title: Kogarkoite, a new natural phase in the system Na2SO4 - NaF - NaCl
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compound: <missing>
pub_title: The crystallography and structure of eitelite, Na2Mg(CO3)2
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pub_title: Crystal structure refinement and optical properties of a Ti3+ fassaite from the Allende Meteorite
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pub_title: Crystal structure analysis of synthetic fluorophlogopite
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compound: <missing>
pub_title: The crystal structure of parkerite (Ni3Bi2S2)
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pub_title:
 High-temperature crystal chemistry of hortonolite
 sample #12018 at T = 24 C
 Note: variety hortonolite

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pub_title:
 High-temperature crystal chemistry of hortonolite
 sample #OG2B at T = 24 C
 Note: variety hortonolite

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pub_title:
 High-temperature crystal chemistry of hortonolite
 sample #12052 at T = 24 C
 Note: variety hortonolite

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formula_title: <missing>
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alpha: 90
beta: 90
gamma: 90
cell_volume: 290.296
crystal_density: 3.219
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pub_title:
 The crystal structures of forsterite and hortonolite at several temperatures
 up to 900 C
 T = 25 C

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pub_title:
 High-temperature crystal chemistry of acmite, diopside, hedenbergite, jadeite,
 spodumene, and ureyite
 T = 24 C
 pyroxene

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pub_title:
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pub_title:
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 High-temperature crystal chemistry of acmite, diopside, hedenbergite, jadeite,
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formula: Si Al Li O4
compound: <missing>
pub_title: The crystal structure of beta eucryptite as a function of temperature T = 647 C
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compound: Solvayshall, Roschwitz, Germany
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beta: 90
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pub_title:
 Crystal-structure refinement of cubic boracite
 Note: This is a high-temperature phase of boracite
 T = 400 C

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compound: Clay Canyon, Fairfield, Utah, USA
pub_title: The crystal structure of crandallite
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formula: Ca B2 Si2 O8
compound: <missing>
pub_title: The crystal structure of danburite: A comparison with anorthite, albite, and reedmergnerite
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compound: <missing>
pub_title: The crystal structure of jagowerite: BaAl2P2O8(OH)2
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formula: Ca K2 C2 O6
compound: <missing>
pub_title: Synthesis, properties and structure of K2Ca(CO3)2, buetschliite
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formula: Si Co2 O4
compound: <missing>
pub_title: Crystal structures of three polymorphs of Co2SiO4 olivine
formula_title: Co2SiO4
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compound: <missing>
pub_title: Crystal structures of three polymorphs of Co2SiO4 wadsleyite
formula_title: Co2SiO4
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formula: (Si Co2) O4
compound: <missing>
pub_title: Crystal structures of three polymorphs of Co2SiO4 spinel
formula_title: Co2SiO4
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formula: (Fe2.001 Si.999) O4
compound: Synthetic
pub_title: Crystal structures of spinel polymorphs of Fe2SiO4 and Ni2SiO4
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compound: <missing>
pub_title: Crystal structures of spinel polymorphs of Fe2SiO4 and Ni2SiO4
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formula: Si Al2 Ca O6
compound: <missing>
pub_title: Structure and crystal chemistry of calcium Tschermak's pyroxene, CaAlAlSiO6
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formula: Ca P Be O5 H
compound: <missing>
pub_title: A refinement of the crystal structure of herderite, CaBePO4OH
formula_title: <missing>
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formula: (Mg1.58 Ti.42) B O4
compound: Warwick, Orange County, New York, USA
formula_title: <missing>
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c: 3.085
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pub_title:
 Pinakiolite, Mg2MnO2[BO3]; warwickite, Mg(Mg0.5Ti0.5)O[BO3]; wightmanite,
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formula: Mg.636 Fe1.332 Ca.032 Si2 O6
compound: <missing>
pub_title: The high temperature crystal chemistry of clinohypersthene T = 825 C
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formula: Pb6 Cl6 Cr O8 H4
compound: <missing>
pub_title: The crystal structure and composition of yedlinite
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formula_title: <missing>
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pub_title:
 The crystal structures of gillespite I and II: A structure determination at
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pub_title:
 The crystal structures of gillespite I and II: A structure determination at
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pub_title: Thermal expansion of the pentlandite structure Outokumpu, at 24 deg C
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pub_title: The Crystal Structure of Gillespite II at 26 Kilobars: Correction and Addendum
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formula: Te13 S8 Bi14
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formula_title: <missing>
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pub_title:
 The formula, structure, and chemical bonding of tetradymite, Bi14Te13S8, and the
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 cell parameters were computed from those provided in the rhombohedral setting

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formula_title: <missing>
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gamma: 90
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pub_title:
 The crystal structure of synthetic titanite, CaTiOSiO4, and the domain textures
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formula: Mg O
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formula_title: <missing>
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c: 4.211
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gamma: 90
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pub_title:
 Effects of temperature and pressure on the cell dimension and X-ray temperature
 factors of periclase
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formula_title: <missing>
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pub_title:
 The thermal expansion of diopside to 800 C and a refinement of the crystal
 structure at 700 C
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formula: Ca Ti Si O5
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pub_title:
 High-temperature structural study of the P2_1/a - A2/a phase transition in
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pub_title:
 High-temperature structural study of the P2_1/a - A2/a phase transition in
 synthetic titanite, CaTiSiO5
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pub_title:
 High-temperature structural study of the P2_1/a - A2/a phase transition in
 synthetic titanite, CaTiSiO5
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compound: <missing>
pub_title: The crystal structure of vuagnatite, CaAl(OH)SiO4
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formula: As Zn2 O5 H
compound: <missing>
pub_title: The crystal structure and infrared properties of adamite
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formula: Cu S
compound: Summitville, Colorado
pub_title: Crystal structure refinement of covellite
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formula: Mn7 Si O12
compound: <missing>
formula_title: <missing>
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b: 9.408
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beta: 90
gamma: 90
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pub_title:
 Braunite: its structure and relationship to bixbyite, and some insights on the
 genealogy of fluorite derivative structures

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formula: Si Mg2 O4
compound: <missing>
formula_title: <missing>
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beta: 90
gamma: 90
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pub_title:
 Effects of temperature and pressure on the crystal structure of forsterite
 T = -196 C, P = 1 atm
 olivine

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formula_title: <missing>
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pub_title:
 Effects of temperature and pressure on the crystal structure of forsterite
 T = 23 C, P = 1 atm
 olivine

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formula: Ba Be2 Si2 O7
compound: amazonite pocket, Park County, Colorado, USA
pub_title: Barylite, BaBe2Si2O7: its space group and crystal structure
formula_title: <missing>
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formula: Fe2 Si O4
compound: Synthetic
formula_title: <missing>
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alpha: 90
beta: 90
gamma: 90
cell_volume: 305.603
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pub_title:
 Effects of temperature and pressure on the crystal structure of ferromagnesian
 olivine
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formula: K Si Al O3.996
compound: Larvik, Norway
formula_title: KAlSiO4
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b: 5.153
c: 8.682
alpha: 90
beta: 90
gamma: 120
cell_volume: 199.651
crystal_density: 2.630
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pub_title:
 The structure of KAlSiO4 with P6_3mc symmetry
 Note: natural sample of kalsilite was mixed with powdered KCl and heated,
 it tranformed to this phase

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formula: Ni3 S2
compound: <missing>
pub_title: The crystal structure of heazlewoodite, and metallic bonds in sulfide minerals
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formula: (Ni.97 Co.03) S.98 As.1 Sb.91 Bi.01
compound: <missing>
pub_title: Crystal structure refinement of arsenian ullmannite approximate cubic structure
formula_title: <missing>
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formula: Ca Mg C2 O6
compound: <missing>
formula_title: <missing>
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b: 4.8033
c: 15.984
alpha: 90
beta: 90
gamma: 120
cell_volume: 319.371
crystal_density: 2.876
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pub_title:
 Structural refinements of dolomite and a magnesian calcite and implications for
 dolomite formation in the marine environment

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compound: <missing>
formula_title: <missing>
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b: 4.941
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beta: 90
gamma: 120
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pub_title:
 Structural refinements of dolomite and a magnesian calcite and implications for
 dolomite formation in the marine environment
 Mg-calcite

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pub_title:
 The structure of malayaite, CaSnOSiO4, a tin analog of titanite
 Note: sample is from Red-a-Ven mine, Meldon, Devonshire, England

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formula: Cu Si O4 H2
compound: <missing>
pub_title: A refinement of the structure of dioptase, Cu6[Si6O18]*6H2O Note: sample is from Reneville, Congo
formula_title: <missing>
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c: 7.778
alpha: 90
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cell_volume: 1429.154
crystal_density: 3.297
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formula: Fe24 K6 Li S26 Cl
compound: <missing>
pub_title: X-ray study of K6LiFe24S26Cl, a djerfisherite-like compound
formula_title: K6LiFe24S26Cl
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formula: Fe.5 Mg.5 Ti1.999 O5
compound: <missing>
formula_title: <missing>
a: 9.7762
b: 10.0341
c: 3.7504
alpha: 90
beta: 90
gamma: 90
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crystal_density: 3.896
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pub_title:
 Cation distribution and high-temperature crystal chemistry of armalcolite
 sample Arm-E, T = 24 deg C, before annealing

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compound: <missing>
formula_title: <missing>
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b: 10.0625
c: 3.7422
alpha: 90
beta: 90
gamma: 90
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pub_title:
 Cation distribution and high-temperature crystal chemistry of armalcolite
 sample Arm-E, T = 24 deg C, after annealing

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compound: <missing>
formula_title: <missing>
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b: 10.1835
c: 3.76422
alpha: 90
beta: 90
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crystal_density: 3.778
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pub_title:
 Cation distribution and high-temperature crystal chemistry of armalcolite
 sample Arm-E, T = 1100 deg C

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compound: <missing>
formula_title: <missing>
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b: 10.0410
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beta: 90
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pub_title:
 Cation distribution and high-temperature crystal chemistry of armalcolite
 sample Arm-E, T = 24 deg C, after heating

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formula: (Fe.5 Mg.5) Ti2 O5
compound: <missing>
formula_title: <missing>
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alpha: 90
beta: 90
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pub_title:
 Cation distribution and high-temperature crystal chemistry of armalcolite
 sample Arm-C, T = 400 deg C

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formula: Zn3 As2 O6
compound: <missing>
pub_title: Reinerite, Zn3(AsO3)2: an arsenite with a novel type of Zn-tetrahedral double chain
formula_title: <missing>
a: 6.092
b: 14.407
c: 7.811
alpha: 90
beta: 90
gamma: 90
cell_volume: 685.551
crystal_density: 4.283
atoms_sites: ["Zn1", "Zn2", "As1", "As2", "O1", "O2", "O3", "O4"]
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formula: Fe S2
compound: <missing>
pub_title: Crystal structure refinement of a weakly anisotropic pyrite cubic model
formula_title: <missing>
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c: 5.4166
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beta: 90
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formula: (Mg1.4 Sc.3) Li.3 Si2 O6
compound: <missing>
pub_title: The synthesis and crystal structure of a magnesium-lithium-scandium protopyroxene
formula_title: <missing>
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b: 8.773
c: 5.377
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beta: 90
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formula: Cu I O4 H
compound: Synthetic
formula_title: <missing>
a: 10.784
b: 6.708
c: 4.781
alpha: 90
beta: 90
gamma: 90
cell_volume: 345.853
crystal_density: 4.906
atoms_sites: ["Cu", "I", "O1", "O2", "O-h", "H"]
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pub_title:
 Salesite, CuIO3(OH), and Cu(IO3)2*2H2O: A comparison of the crystal
 structures and their magnetic behavior

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formula: Cu I2 O8 H4
compound: Synthetic
formula_title: Cu(IO3)2*2H2O
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b: 4.813
c: 11.165
alpha: 90
beta: 103.34
gamma: 90
cell_volume: 351.788
crystal_density: 4.242
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pub_title:
 Salesite, CuIO3(OH), and Cu(IO3)2*2H2O: A comparison of the crystal
 structures and their magnetic behavior

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formula: Cu4 O3
compound: <missing>
pub_title: The crystal structure of paramelaconite, Cu4O3
formula_title: <missing>
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b: 5.837
c: 9.932
alpha: 90
beta: 90
gamma: 90
cell_volume: 338.389
crystal_density: 5.931
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formula: Sn S2
compound: <missing>
formula_title: <missing>
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b: 3.638
c: 5.880
alpha: 90
beta: 90
gamma: 120
cell_volume: 67.396
crystal_density: 4.505
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pub_title:
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formula: Zr Si O4
compound: <missing>
pub_title: Crystal structure and compressibility of zircon at high pressure crystal No. 1, 1 atm - before P
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formula: Al2 Si O5
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formula_title: Ni2SiO4
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pub_title:
 Crystal structures and electron densities of nickel and iron silicate spinels at
 elevated temperature or pressure
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formula: Fe2 Si O4
compound: Synthetic
formula_title: <missing>
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pub_title:
 Crystal structures and electron densities of nickel and iron silicate spinels at
 elevated temperature or pressure

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formula: Cu S2
compound: Synthetic
pub_title: Structure and symmetry of CuS2 (pyrite structure)
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formula: (Ni.86 Co.14) S Sb
compound: <missing>
pub_title: Crystal structure refinement of a cobaltian ullmannite
formula_title: <missing>
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formula: Ca2.94 Mg.38 Zr1.21 Ti.47 (Si1.509 Al.999 Fe.492) O12
compound: <missing>
pub_title: Crystal chemistry of kimzeyite from Stomboli, Aeolian Islands, Italy
formula_title: <missing>
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formula: Pb2 As2 O5
compound: <missing>
pub_title: The crystal structure of paulmooreite, Pb2[As2O5]: dimeric arsenite groups
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formula: Zn2 As O5
compound: <missing>
pub_title: Crystal structure of paradamite
formula_title: <missing>
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formula: K Fe2 S3
compound: <missing>
pub_title: Crystal structure of rasvumite, KFe2S3
formula_title: <missing>
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b: 11.019
c: 5.431
alpha: 90
beta: 90
gamma: 90
cell_volume: 541.530
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formula: Na Fe S2 (O2 H4)
compound: Coyote Peak, Humboldt County, California, USA
pub_title: The crystal structure of erdite, NaFeS2*2H2O
formula_title: <missing>
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c: 5.507
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formula: Fe Ni
compound: Cape Town iron meteorite
pub_title: Tetrataenite - ordered FeNi, a new mineral in meteorites
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formula: Si O2
compound: <missing>
pub_title: Structure and elastic properties of quartz at pressure P = 1 atm
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b: 4.916
c: 5.4054
alpha: 90
beta: 90
gamma: 120
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formula: Mg1.03 Mn.97 Si O4
compound: Langban, Sweden
pub_title: The forsterite-tephroite series: I. Crystal structure refinements Sample: Fo51 olivine
formula_title: <missing>
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b: 10.491
c: 6.123
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formula: Mn1.83 Mg.17 Si O4
compound: Madagascar
pub_title: The forsterite-tephroite series: I. Crystal structure refinements Sample: Te 91 olivine
formula_title: <missing>
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b: 10.589
c: 6.234
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compound: <missing>
formula_title: <missing>
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b: 8.93
c: 5.27
alpha: 90
beta: 106.44
gamma: 90
cell_volume: 440.538
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pub_title:
 Exsolution relationships in a clinopyroxene of average composition
 Ca0.43Mn0.69Mg0.82Si2O6: X-ray diffraction and analytical electron microscopy

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compound: Anderson mine, Yavapai County, Arizona, USA
pub_title: The crystal chemistry of the uranyl silicate minerals
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formula: Ti V O4 H
compound: Lake View mine, Kalgoorlie, Western Australia
formula_title: <missing>
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pub_title:
 Tivanite, a new oxyhydroxide mineral from Western Australia,
 and its structural relationship to rutile and diaspore

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formula: (Fe.725 Ni.025 Si.25)
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formula: Bi.138 Cu1.344 S
compound: <missing>
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formula: Si2 Mg3 O9 H4
compound: <missing>
pub_title: The crystal structure of lizardite 1T: hydrogen bonds and polytypism
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formula: Si Mg O3
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formula: Hf Si O4
compound: <missing>
formula_title: <missing>
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beta: 90
gamma: 90
cell_volume: 257.597
crystal_density: 6.977
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pub_title:
 Crystal structure of synthetic hafnon, HfSiO4, comparison with zircon and the
 actinide orthosilicates

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pub_title: A further crystal structure refinement of cobaltite
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formula: (Fe.19 Co.27 Ni.54) (As1.04 S.96)
compound: Garson mine, Sudbury, Ontario, Canada
pub_title: A further crystal structure refinement of gersdorffite Sample: M15861
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formula: Ag Hg As S3
compound: <missing>
pub_title: Laffittite, AgHgAsS3: crystal structure and second occurrence from the Getchell mine, Nevada
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formula: Mn.89 Al2.11 O4
compound: <missing>
formula_title: <missing>
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beta: 90
gamma: 90
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pub_title:
 Crystal chemistry and petrology of coexisting galaxite and jacobsite and other
 spinel solution and solvi

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compound: <missing>
formula_title: K2SiSi3O9
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beta: 90
gamma: 120
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crystal_density: 3.086
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pub_title:
 The crystal structure of K2SiSi3O9
 Note: B(1,2) for K and Si1 have been changed to match symmetry constraints
 Note: wadeite structure

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formula: Ba Fe Si4 O10
compound: Fresno Co, California, USA
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pub_title:
 High-pressure and high-temperature crystallographic study of the gillespite I-II
 phase transition
 P = 1 bar

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pub_title: Structure refinements of some thermally disordered dolomites sample EU
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compound: <missing>
pub_title: Structure refinements of some thermally disordered dolomites sample DO - 1050
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pub_title: Structure refinements of some thermally disordered dolomites sample DO - 1100
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formula: Na.956 Zr Be.5 P2 O8
compound: <missing>
pub_title: Gainesite, sodium zirconium beryllophosphate: A new mineral and its crystal structure
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formula: Ca Ge O3
compound: <missing>
formula_title: CaGeO3
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c: 7.4452
alpha: 90
beta: 90
gamma: 90
cell_volume: 206.363
crystal_density: 5.172
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pub_title:
 The crystal structure of CaGeO3 perovskite and the crystal chemistry of the
 GdFeO3-type perovskites

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compound: <missing>
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formula: Fe Si O3
compound: <missing>
pub_title: The crystal structure of high clinoferrosilicate T = 1050 C
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formula: Al2 Si O5
compound: <missing>
pub_title: Compressibility and crystal structure of andalusite at high pressure 12 kbar continuous-scan
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formula: Ca Ti Si O5
compound: <missing>
pub_title: The crystal structure of an Al-rich titanite from Grisons, Switzerland
formula_title: <missing>
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formula: Fe3 O4
compound: Synthetic
formula_title: <missing>
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b: 8.3958
c: 8.3958
alpha: 90
beta: 90
gamma: 90
cell_volume: 591.815
crystal_density: 5.197
atoms_sites: ["FeA", "FeB", "O"]
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pub_title:
 Crystal structure and cation distribution in titanomagnetites (Fe3-xTixO4)
 Note: Sample ID: MT100-1350

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pub_title: High-temperature structure refinements of calcite and magnesite Sample: T = 24 C
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pub_title: The crystal chemistry of iron-nickel thiospinels Note: structure from ICSD
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pub_title: Crystal structure refinement of huntite, CaMg3(CO3)4, with X-ray powder data
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