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Result of symbol lookup:
Space group number: 144
Schoenflies symbol: C3^2
Hermann-Mauguin symbol: P 31
Hall symbol: P 31
Input space group symbol: P 31
Convention: Default
Number of lattice translations: 1
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 3
Total number of symmetry operations: 3
Parallelepiped containing an asymmetric unit:
0<=x<1; 0<=y<1; 0<=z<1/3
List of symmetry operations:
| Matrix
| Rotation-part type
| Axis direction
| Screw/glide component
| Origin shift
|
| x,y,z
| 1 | - | - | -
|
| -y,x-y,z+1/3
| 3^1 | [0,0,1] | 0,0,1/3 | 0,0,0
|
| -x+y,-x,z+2/3
| 3^-1 | [0,0,1] | 0,0,2/3 | 0,0,0
|
List of Wyckoff positions:
| Wyckoff letter
| Multiplicity
| Site symmetry
point group type
| Representative special position operator
|
| a | 3 | 1 | x,y,z
|
Harker planes:
| Algebraic
| Normal vector
| A point in the plane
|
| x-y,-x-2*y,1/3 | [0,0,1] | 0,0,1/3
|
Additional generators of Euclidean normalizer:
Number of structure-seminvariant vectors and moduli: 2
Vector Modulus
(0, 0, 1) 0
(1, 2, 0) 3
Further generators:
| Matrix
| Rotation-part type
| Axis direction
| Screw/glide component
| Origin shift
|
| -x,-y,z
| 2 | [0,0,1] | 0,0,0 | 0,0,0
|
| y,x,-z
| 2 | [1,1,0] | 0,0,0 | 0,0,0
|
Grid factors implied by symmetries:
Space group: (1, 1, 3)
Structure-seminvariant vectors and moduli: (3, 3, 1)
Euclidean normalizer: (3, 3, 3)
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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