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Result of symbol lookup:
Space group number: 58
Schoenflies symbol: D2h^12
Hermann-Mauguin symbol: P n n m
Hall symbol: -P 2 2n
Input space group symbol: P n n m
Convention: Default
Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 4
Total number of symmetry operations: 8
Parallelepiped containing an asymmetric unit:
0<=x<1; 0<=y<=1/4; 0<=z<=1/2
List of symmetry operations:
Matrix
| Rotation-part type
| Axis direction
| Screw/glide component
| Origin shift
|
x,y,z
| 1 | - | - | -
|
-x,-y,z
| 2 | [0,0,1] | 0,0,0 | 0,0,0
|
x+1/2,-y+1/2,-z+1/2
| 2 | [1,0,0] | 1/2,0,0 | 0,1/4,1/4
|
-x+1/2,y+1/2,-z+1/2
| 2 | [0,1,0] | 0,1/2,0 | 1/4,0,1/4
|
-x,-y,-z
| -1 | - | - | 0,0,0
|
x,y,-z
| -2 | [0,0,1] | 0,0,0 | 0,0,0
|
-x-1/2,y-1/2,z-1/2
| -2 | [1,0,0] | 0,-1/2,-1/2 | -1/4,0,0
|
x-1/2,-y-1/2,z-1/2
| -2 | [0,1,0] | -1/2,0,-1/2 | 0,-1/4,0
|
List of Wyckoff positions:
Wyckoff letter
| Multiplicity
| Site symmetry point group type
| Representative special position operator
|
h | 8 | 1 | x,y,z
|
g | 4 | m | x,y,0
|
f | 4 | 2 | 0,1/2,z
|
e | 4 | 2 | 0,0,z
|
d | 2 | 2/m | 0,1/2,1/2
|
c | 2 | 2/m | 0,1/2,0
|
b | 2 | 2/m | 0,0,1/2
|
a | 2 | 2/m | 0,0,0
|
Harker planes:
Algebraic
| Normal vector
| A point in the plane
|
2*x,2*y,0 | [0,0,1] | 0,0,0
|
1/2,2*y+1/2,2*z+1/2 | [1,0,0] | 1/2,1/2,1/2
|
2*x+1/2,1/2,2*z+1/2 | [0,1,0] | 1/2,1/2,1/2
|
Additional generators of Euclidean normalizer:
Number of structure-seminvariant vectors and moduli: 3
Vector Modulus
(1, 0, 0) 2
(0, 1, 0) 2
(0, 0, 1) 2
Grid factors implied by symmetries:
Space group: (2, 2, 2)
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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