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Input space group symbol: H -6 -2
Convention: Hall symbol
Number of lattice translations: 3
Space group is acentric.
Number of representative symmetry operations: 12
Total number of symmetry operations: 36
Parallelepiped containing an asymmetric unit:
cctbx Error: Brick is not available for the given space group representation.
List of symmetry operations:
| Matrix
| Rotation-part type
| Axis direction
| Screw/glide component
| Origin shift
|
| x,y,z
| 1 | - | - | -
|
| -x+y,-x,-z
| -6^1 | [0,0,1] | 0,0,0 | 0,0,0
|
| -y,x-y,z
| 3^1 | [0,0,1] | 0,0,0 | 0,0,0
|
| x,y,-z
| -2 | [0,0,1] | 0,0,0 | 0,0,0
|
| -x+y,-x,z
| 3^-1 | [0,0,1] | 0,0,0 | 0,0,0
|
| -y,x-y,-z
| -6^-1 | [0,0,1] | 0,0,0 | 0,0,0
|
| y,x,z
| -2 | [-1,1,0] | 0,0,0 | 0,0,0
|
| x-y,-y,-z
| 2 | [1,0,0] | 0,0,0 | 0,0,0
|
| -x,-x+y,z
| -2 | [2,1,0] | 0,0,0 | 0,0,0
|
| y,x,-z
| 2 | [1,1,0] | 0,0,0 | 0,0,0
|
| x-y,-y,z
| -2 | [1,2,0] | 0,0,0 | 0,0,0
|
| -x,-x+y,-z
| 2 | [0,1,0] | 0,0,0 | 0,0,0
|
| x+2/3,y+1/3,z
| 1 | - | - | -
|
| -x+y+2/3,-x+1/3,-z
| -6^1 | [0,0,1] | 0,0,0 | 1/3,0,0
|
| -y+2/3,x-y+1/3,z
| 3^1 | [0,0,1] | 0,0,0 | 1/3,1/3,0
|
| x+2/3,y+1/3,-z
| -2 | [0,0,1] | 2/3,1/3,0 | 0,0,0
|
| -x+y+2/3,-x+1/3,z
| 3^-1 | [0,0,1] | 0,0,0 | 1/3,0,0
|
| -y+2/3,x-y+1/3,-z
| -6^-1 | [0,0,1] | 0,0,0 | 1/3,1/3,0
|
| y+2/3,x+1/3,z
| -2 | [-1,1,0] | 1/2,1/2,0 | 1/6,0,0
|
| x-y+2/3,-y+1/3,-z
| 2 | [1,0,0] | 1/2,0,0 | 0,1/6,0
|
| -x+2/3,-x+y+1/3,z
| -2 | [2,1,0] | 0,0,0 | 1/3,0,0
|
| y+2/3,x+1/3,-z
| 2 | [1,1,0] | 1/2,1/2,0 | 1/6,0,0
|
| x-y+2/3,-y+1/3,z
| -2 | [1,2,0] | 1/2,0,0 | 0,1/6,0
|
| -x+2/3,-x+y+1/3,-z
| 2 | [0,1,0] | 0,0,0 | 1/3,0,0
|
| x+1/3,y+2/3,z
| 1 | - | - | -
|
| -x+y+1/3,-x+2/3,-z
| -6^1 | [0,0,1] | 0,0,0 | 1/3,1/3,0
|
| -y+1/3,x-y+2/3,z
| 3^1 | [0,0,1] | 0,0,0 | 0,1/3,0
|
| x+1/3,y+2/3,-z
| -2 | [0,0,1] | 1/3,2/3,0 | 0,0,0
|
| -x+y+1/3,-x+2/3,z
| 3^-1 | [0,0,1] | 0,0,0 | 1/3,1/3,0
|
| -y+1/3,x-y+2/3,-z
| -6^-1 | [0,0,1] | 0,0,0 | 0,1/3,0
|
| y+1/3,x+2/3,z
| -2 | [-1,1,0] | 1/2,1/2,0 | -1/6,0,0
|
| x-y+1/3,-y+2/3,-z
| 2 | [1,0,0] | 0,0,0 | 0,1/3,0
|
| -x+1/3,-x+y+2/3,z
| -2 | [2,1,0] | 0,1/2,0 | 1/6,0,0
|
| y+1/3,x+2/3,-z
| 2 | [1,1,0] | 1/2,1/2,0 | -1/6,0,0
|
| x-y+1/3,-y+2/3,z
| -2 | [1,2,0] | 0,0,0 | 0,1/3,0
|
| -x+1/3,-x+y+2/3,-z
| 2 | [0,1,0] | 0,1/2,0 | 1/6,0,0
|
Space group number: 187
Conventional Hermann-Mauguin symbol: P -6 m 2
Universal Hermann-Mauguin symbol: P -6 m 2 (2*a+b,-a+b,c)
Hall symbol: P -6 2 (1/3*x+1/3*y,-1/3*x+2/3*y,z)
Change-of-basis matrix: 2*x-y,x+y,z
Inverse: 1/3*x+1/3*y,-1/3*x+2/3*y,z
List of Wyckoff positions:
| Wyckoff letter
| Multiplicity
| Site symmetry
point group type
| Representative special position operator
|
| o | 36 | 1 | x,y,z
|
| n | 18 | m | 0,y,z
|
| m | 18 | m | x,y,1/2
|
| l | 18 | m | x,y,0
|
| k | 9 | mm2 | 0,y,1/2
|
| j | 9 | mm2 | 0,y,0
|
| i | 6 | 3m | 0,1/3,z
|
| h | 6 | 3m | 0,-1/3,z
|
| g | 6 | 3m | 0,0,z
|
| f | 3 | -62m | 0,1/3,1/2
|
| e | 3 | -62m | 0,1/3,0
|
| d | 3 | -62m | 0,-1/3,1/2
|
| c | 3 | -62m | 0,-1/3,0
|
| b | 3 | -62m | 0,0,1/2
|
| a | 3 | -62m | 0,0,0
|
Harker planes:
| Algebraic
| Normal vector
| A point in the plane
|
| x-y,-x-2*y,0 | [0,0,1] | 0,0,0
|
| y,2*y,2*z | [1,0,0] | 0,0,0
|
| x+y,-x-y,2*z | [1,1,0] | 0,0,0
|
| 2*x,x,2*z | [0,1,0] | 0,0,0
|
Additional generators of Euclidean normalizer:
Number of structure-seminvariant vectors and moduli: 1
Vector Modulus
(2, 0, 3) 6
Inversion through a centre at: 0,0,0
Grid factors implied by symmetries:
Space group: (3, 3, 1)
Structure-seminvariant vectors and moduli: (3, 1, 2)
Euclidean normalizer: (3, 3, 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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