[Index of services] [New input]
Input space group symbol: H -6c -2c
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+1/2 -6^1[0,0,1]0,0,00,0,1/4
-y,x-y,z 3^1[0,0,1]0,0,00,0,0
x,y,-z+1/2 -2[0,0,1]0,0,00,0,1/4
-x+y,-x,z 3^-1[0,0,1]0,0,00,0,0
-y,x-y,-z+1/2 -6^-1[0,0,1]0,0,00,0,1/4
y,x,z+1/2 -2[-1,1,0]0,0,1/20,0,0
x-y,-y,-z 2[1,0,0]0,0,00,0,0
-x,-x+y,z+1/2 -2[2,1,0]0,0,1/20,0,0
y,x,-z 2[1,1,0]0,0,00,0,0
x-y,-y,z+1/2 -2[1,2,0]0,0,1/20,0,0
-x,-x+y,-z 2[0,1,0]0,0,00,0,0
x+2/3,y+1/3,z 1---
-x+y+2/3,-x+1/3,-z+1/2 -6^1[0,0,1]0,0,01/3,0,1/4
-y+2/3,x-y+1/3,z 3^1[0,0,1]0,0,01/3,1/3,0
x+2/3,y+1/3,-z+1/2 -2[0,0,1]2/3,1/3,00,0,1/4
-x+y+2/3,-x+1/3,z 3^-1[0,0,1]0,0,01/3,0,0
-y+2/3,x-y+1/3,-z+1/2 -6^-1[0,0,1]0,0,01/3,1/3,1/4
y+2/3,x+1/3,z+1/2 -2[-1,1,0]1/2,1/2,1/21/6,0,0
x-y+2/3,-y+1/3,-z 2[1,0,0]1/2,0,00,1/6,0
-x+2/3,-x+y+1/3,z+1/2 -2[2,1,0]0,0,1/21/3,0,0
y+2/3,x+1/3,-z 2[1,1,0]1/2,1/2,01/6,0,0
x-y+2/3,-y+1/3,z+1/2 -2[1,2,0]1/2,0,1/20,1/6,0
-x+2/3,-x+y+1/3,-z 2[0,1,0]0,0,01/3,0,0
x+1/3,y+2/3,z 1---
-x+y+1/3,-x+2/3,-z+1/2 -6^1[0,0,1]0,0,01/3,1/3,1/4
-y+1/3,x-y+2/3,z 3^1[0,0,1]0,0,00,1/3,0
x+1/3,y+2/3,-z+1/2 -2[0,0,1]1/3,2/3,00,0,1/4
-x+y+1/3,-x+2/3,z 3^-1[0,0,1]0,0,01/3,1/3,0
-y+1/3,x-y+2/3,-z+1/2 -6^-1[0,0,1]0,0,00,1/3,1/4
y+1/3,x+2/3,z+1/2 -2[-1,1,0]1/2,1/2,1/2-1/6,0,0
x-y+1/3,-y+2/3,-z 2[1,0,0]0,0,00,1/3,0
-x+1/3,-x+y+2/3,z+1/2 -2[2,1,0]0,1/2,1/21/6,0,0
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+1/2 -2[1,2,0]0,0,1/20,1/3,0
-x+1/3,-x+y+2/3,-z 2[0,1,0]0,1/2,01/6,0,0

Space group number: 188
Conventional Hermann-Mauguin symbol: P -6 c 2
Universal    Hermann-Mauguin symbol: P -6 c 2 (2*a+b,-a+b,c)
Hall symbol:  P -6c 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
l361x,y,z
k18mx,y,1/4
j1820,y,0
i1230,1/3,z
h1230,-1/3,z
g1230,0,z
f6-60,1/3,1/4
e6320,1/3,0
d6-60,-1/3,1/4
c6320,-1/3,0
b6-60,0,1/4
a6320,0,0

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, 2)
  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.


[Index of services] [New input]