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Result of symbol lookup:
Space group number: 221
Schoenflies symbol: Oh^1
Hermann-Mauguin symbol: P m -3 m
Hall symbol: -P 4 2 3
Input space group symbol: P m -3 m
Convention: Default
Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 24
Total number of symmetry operations: 48
Parallelepiped containing an asymmetric unit:
0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
List of symmetry operations:
| Matrix
| Rotation-part type
| Axis direction
| Screw/glide component
| Origin shift
|
| x,y,z
| 1 | - | - | -
|
| -y,x,z
| 4^1 | [0,0,1] | 0,0,0 | 0,0,0
|
| -x,-y,z
| 2 | [0,0,1] | 0,0,0 | 0,0,0
|
| y,-x,z
| 4^-1 | [0,0,1] | 0,0,0 | 0,0,0
|
| x,-y,-z
| 2 | [1,0,0] | 0,0,0 | 0,0,0
|
| y,x,-z
| 2 | [1,1,0] | 0,0,0 | 0,0,0
|
| -x,y,-z
| 2 | [0,1,0] | 0,0,0 | 0,0,0
|
| -y,-x,-z
| 2 | [-1,1,0] | 0,0,0 | 0,0,0
|
| z,x,y
| 3^1 | [1,1,1] | 0,0,0 | 0,0,0
|
| -x,z,y
| 2 | [0,1,1] | 0,0,0 | 0,0,0
|
| -z,-x,y
| 3^-1 | [-1,1,1] | 0,0,0 | 0,0,0
|
| x,-z,y
| 4^1 | [1,0,0] | 0,0,0 | 0,0,0
|
| z,-x,-y
| 3^-1 | [1,-1,1] | 0,0,0 | 0,0,0
|
| x,z,-y
| 4^-1 | [1,0,0] | 0,0,0 | 0,0,0
|
| -z,x,-y
| 3^1 | [-1,-1,1] | 0,0,0 | 0,0,0
|
| -x,-z,-y
| 2 | [0,-1,1] | 0,0,0 | 0,0,0
|
| y,z,x
| 3^-1 | [1,1,1] | 0,0,0 | 0,0,0
|
| y,-z,-x
| 3^-1 | [-1,-1,1] | 0,0,0 | 0,0,0
|
| z,y,-x
| 4^1 | [0,1,0] | 0,0,0 | 0,0,0
|
| -y,z,-x
| 3^1 | [-1,1,1] | 0,0,0 | 0,0,0
|
| -z,-y,-x
| 2 | [-1,0,1] | 0,0,0 | 0,0,0
|
| -y,-z,x
| 3^1 | [1,-1,1] | 0,0,0 | 0,0,0
|
| z,-y,x
| 2 | [1,0,1] | 0,0,0 | 0,0,0
|
| -z,y,x
| 4^-1 | [0,1,0] | 0,0,0 | 0,0,0
|
| -x,-y,-z
| -1 | - | - | 0,0,0
|
| y,-x,-z
| -4^1 | [0,0,1] | 0,0,0 | 0,0,0
|
| x,y,-z
| -2 | [0,0,1] | 0,0,0 | 0,0,0
|
| -y,x,-z
| -4^-1 | [0,0,1] | 0,0,0 | 0,0,0
|
| -x,y,z
| -2 | [1,0,0] | 0,0,0 | 0,0,0
|
| -y,-x,z
| -2 | [1,1,0] | 0,0,0 | 0,0,0
|
| x,-y,z
| -2 | [0,1,0] | 0,0,0 | 0,0,0
|
| y,x,z
| -2 | [-1,1,0] | 0,0,0 | 0,0,0
|
| -z,-x,-y
| -3^1 | [1,1,1] | 0,0,0 | 0,0,0
|
| x,-z,-y
| -2 | [0,1,1] | 0,0,0 | 0,0,0
|
| z,x,-y
| -3^-1 | [-1,1,1] | 0,0,0 | 0,0,0
|
| -x,z,-y
| -4^1 | [1,0,0] | 0,0,0 | 0,0,0
|
| -z,x,y
| -3^-1 | [1,-1,1] | 0,0,0 | 0,0,0
|
| -x,-z,y
| -4^-1 | [1,0,0] | 0,0,0 | 0,0,0
|
| z,-x,y
| -3^1 | [-1,-1,1] | 0,0,0 | 0,0,0
|
| x,z,y
| -2 | [0,-1,1] | 0,0,0 | 0,0,0
|
| -y,-z,-x
| -3^-1 | [1,1,1] | 0,0,0 | 0,0,0
|
| -y,z,x
| -3^-1 | [-1,-1,1] | 0,0,0 | 0,0,0
|
| -z,-y,x
| -4^1 | [0,1,0] | 0,0,0 | 0,0,0
|
| y,-z,x
| -3^1 | [-1,1,1] | 0,0,0 | 0,0,0
|
| z,y,x
| -2 | [-1,0,1] | 0,0,0 | 0,0,0
|
| y,z,-x
| -3^1 | [1,-1,1] | 0,0,0 | 0,0,0
|
| -z,y,-x
| -2 | [1,0,1] | 0,0,0 | 0,0,0
|
| z,-y,-x
| -4^-1 | [0,1,0] | 0,0,0 | 0,0,0
|
List of Wyckoff positions:
| Wyckoff letter
| Multiplicity
| Site symmetry
point group type
| Representative special position operator
|
| n | 48 | 1 | x,y,z
|
| m | 24 | m | x,x,z
|
| l | 24 | m | 1/2,y,z
|
| k | 24 | m | 0,y,z
|
| j | 12 | mm2 | 1/2,y,y
|
| i | 12 | mm2 | 0,y,y
|
| h | 12 | mm2 | x,1/2,0
|
| g | 8 | 3m | x,x,x
|
| f | 6 | 4mm | x,1/2,1/2
|
| e | 6 | 4mm | x,0,0
|
| d | 3 | 4/mmm | 1/2,0,0
|
| c | 3 | 4/mmm | 0,1/2,1/2
|
| b | 1 | m-3m | 1/2,1/2,1/2
|
| a | 1 | m-3m | 0,0,0
|
Harker planes:
| Algebraic
| Normal vector
| A point in the plane
|
| x-y,-x-y,0 | [0,0,1] | 0,0,0
|
| 0,2*y,2*z | [1,0,0] | 0,0,0
|
| x+y,-x-y,2*z | [1,1,0] | 0,0,0
|
| 2*x,0,2*z | [0,1,0] | 0,0,0
|
| x+y,x+y,2*z | [-1,1,0] | 0,0,0
|
| x+z,-x-y,y-z | [1,1,1] | 0,0,0
|
| 2*x,y+z,-y-z | [0,1,1] | 0,0,0
|
| x+z,-x-y,-y+z | [-1,-1,1] | 0,0,0
|
| 2*x,y+z,y+z | [0,-1,1] | 0,0,0
|
| x+y,y-z,x+z | [-1,1,1] | 0,0,0
|
| x+z,2*y,x+z | [-1,0,1] | 0,0,0
|
| x+y,y-z,-x-z | [1,-1,1] | 0,0,0
|
| x+z,2*y,-x-z | [1,0,1] | 0,0,0
|
Additional generators of Euclidean normalizer:
Number of structure-seminvariant vectors and moduli: 1
Vector Modulus
(1, 1, 1) 2
Grid factors implied by symmetries:
Space group: (1, 1, 1)
Structure-seminvariant vectors and moduli: (2, 2, 2)
Euclidean normalizer: (2, 2, 2)
All points of a grid over the unit cell are mapped
exactly onto other grid points only if the factors
shown above are factors of the grid.
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