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Result of symbol lookup:
Space group number: 104
Schoenflies symbol: C4v^6
Hermann-Mauguin symbol: P 4 n c
Hall symbol: P 4 -2n
Input space group symbol: P 4 n c
Convention: Default
Number of lattice translations: 1
Space group is acentric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 8
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+1/2,y+1/2,z+1/2
| -2 | [1,0,0] | 0,1/2,1/2 | 1/4,0,0
|
-y+1/2,-x+1/2,z+1/2
| -2 | [1,1,0] | 0,0,1/2 | 1/2,0,0
|
x+1/2,-y+1/2,z+1/2
| -2 | [0,1,0] | 1/2,0,1/2 | 0,1/4,0
|
y+1/2,x+1/2,z+1/2
| -2 | [-1,1,0] | 1/2,1/2,1/2 | 0,0,0
|
List of Wyckoff positions:
Wyckoff letter
| Multiplicity
| Site symmetry point group type
| Representative special position operator
|
c | 8 | 1 | x,y,z
|
b | 4 | 2 | 0,1/2,z
|
a | 2 | 4 | 0,0,z
|
Harker planes:
Algebraic
| Normal vector
| A point in the plane
|
x-y,-x-y,0 | [0,0,1] | 0,0,0
|
Additional generators of Euclidean normalizer:
Number of structure-seminvariant vectors and moduli: 2
Vector Modulus
(0, 0, 1) 0
(1, 1, 0) 2
Inversion through a centre at: 0,0,0
Grid factors implied by symmetries:
Space group: (2, 2, 2)
Structure-seminvariant vectors and moduli: (2, 2, 1)
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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