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Result of symbol lookup:
Space group number: 64
Schoenflies symbol: D2h^18
Hermann-Mauguin symbol: C m c a
Hall symbol: -C 2ac 2
Input space group symbol: C m c a
Convention: Default
Number of lattice translations: 2
Space group is centric.
Number of representative symmetry operations: 4
Total number of symmetry operations: 16
Parallelepiped containing an asymmetric unit:
0<=x<=1/4; 0<=y<=1/4; 0<=z<1
List of symmetry operations:
Matrix
| Rotation-part type
| Axis direction
| Screw/glide component
| Origin shift
|
x,y,z
| 1 | - | - | -
|
-x+1/2,-y,z+1/2
| 2 | [0,0,1] | 0,0,1/2 | 1/4,0,0
|
x,-y,-z
| 2 | [1,0,0] | 0,0,0 | 0,0,0
|
-x+1/2,y,-z+1/2
| 2 | [0,1,0] | 0,0,0 | 1/4,0,1/4
|
-x,-y,-z
| -1 | - | - | 0,0,0
|
x-1/2,y,-z-1/2
| -2 | [0,0,1] | -1/2,0,0 | 0,0,-1/4
|
-x,y,z
| -2 | [1,0,0] | 0,0,0 | 0,0,0
|
x-1/2,-y,z-1/2
| -2 | [0,1,0] | -1/2,0,-1/2 | 0,0,0
|
x+1/2,y+1/2,z
| 1 | - | - | -
|
-x+1,-y+1/2,z+1/2
| 2 | [0,0,1] | 0,0,1/2 | 1/2,1/4,0
|
x+1/2,-y+1/2,-z
| 2 | [1,0,0] | 1/2,0,0 | 0,1/4,0
|
-x+1,y+1/2,-z+1/2
| 2 | [0,1,0] | 0,1/2,0 | 1/2,0,1/4
|
-x+1/2,-y+1/2,-z
| -1 | - | - | 1/4,1/4,0
|
x,y+1/2,-z-1/2
| -2 | [0,0,1] | 0,1/2,0 | 0,0,-1/4
|
-x+1/2,y+1/2,z
| -2 | [1,0,0] | 0,1/2,0 | 1/4,0,0
|
x,-y+1/2,z-1/2
| -2 | [0,1,0] | 0,0,-1/2 | 0,1/4,0
|
List of Wyckoff positions:
Wyckoff letter
| Multiplicity
| Site symmetry point group type
| Representative special position operator
|
g | 16 | 1 | x,y,z
|
f | 8 | m | 0,y,z
|
e | 8 | 2 | 1/4,y,1/4
|
d | 8 | 2 | x,0,0
|
c | 8 | -1 | 1/4,1/4,0
|
b | 4 | 2/m | 1/2,0,0
|
a | 4 | 2/m | 0,0,0
|
Harker planes:
Algebraic
| Normal vector
| A point in the plane
|
2*x+1/2,2*y,1/2 | [0,0,1] | 1/2,0,1/2
|
0,2*y,2*z | [1,0,0] | 0,0,0
|
2*x+1/2,0,2*z+1/2 | [0,1,0] | 1/2,0,1/2
|
Additional generators of Euclidean normalizer:
Number of structure-seminvariant vectors and moduli: 2
Vector Modulus
(1, 0, 0) 2
(0, 0, 1) 2
Grid factors implied by symmetries:
Space group: (2, 2, 2)
Structure-seminvariant vectors and moduli: (2, 1, 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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