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Result of symbol lookup:
  Space group number: 167
  Schoenflies symbol: D3d^6
  Hermann-Mauguin symbol: R -3 c
  Trigonal using hexagonal axes
  Hall symbol: -R 3 2"c

Input space group symbol: R -3 c :H
Convention: Default

Number of lattice translations: 3
Space group is centric.
Number of representative symmetry operations: 6
Total number of symmetry operations: 36

Parallelepiped containing an asymmetric unit:
  0<=x<=1/3; -1/6<=y<=0; 1/12<=z<=7/12

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y,x-y,z 3^1[0,0,1]0,0,00,0,0
-x+y,-x,z 3^-1[0,0,1]0,0,00,0,0
y,x,-z+1/2 2[1,1,0]0,0,00,0,1/4
-x,-x+y,-z+1/2 2[0,1,0]0,0,00,0,1/4
x-y,-y,-z+1/2 2[1,0,0]0,0,00,0,1/4
-x,-y,-z -1--0,0,0
y,-x+y,-z -3^1[0,0,1]0,0,00,0,0
x-y,x,-z -3^-1[0,0,1]0,0,00,0,0
-y,-x,z-1/2 -2[1,1,0]0,0,-1/20,0,0
x,x-y,z-1/2 -2[0,1,0]0,0,-1/20,0,0
-x+y,y,z-1/2 -2[1,0,0]0,0,-1/20,0,0
x+2/3,y+1/3,z+1/3 1---
-y+2/3,x-y+1/3,z+1/3 3^1[0,0,1]0,0,1/31/3,1/3,0
-x+y+2/3,-x+1/3,z+1/3 3^-1[0,0,1]0,0,1/31/3,0,0
y+2/3,x+1/3,-z+5/6 2[1,1,0]1/2,1/2,01/6,0,5/12
-x+2/3,-x+y+1/3,-z+5/6 2[0,1,0]0,0,01/3,0,5/12
x-y+2/3,-y+1/3,-z+5/6 2[1,0,0]1/2,0,00,1/6,5/12
-x+2/3,-y+1/3,-z+1/3 -1--1/3,1/6,1/6
y+2/3,-x+y+1/3,-z+1/3 -3^1[0,0,1]0,0,01/3,-1/3,1/6
x-y+2/3,x+1/3,-z+1/3 -3^-1[0,0,1]0,0,01/3,2/3,1/6
-y+2/3,-x+1/3,z-1/6 -2[1,1,0]1/6,-1/6,-1/61/2,0,0
x+2/3,x-y+1/3,z-1/6 -2[0,1,0]2/3,1/3,-1/60,0,0
-x+y+2/3,y+1/3,z-1/6 -2[1,0,0]1/6,1/3,-1/61/4,0,0
x+1/3,y+2/3,z+2/3 1---
-y+1/3,x-y+2/3,z+2/3 3^1[0,0,1]0,0,2/30,1/3,0
-x+y+1/3,-x+2/3,z+2/3 3^-1[0,0,1]0,0,2/31/3,1/3,0
y+1/3,x+2/3,-z+7/6 2[1,1,0]1/2,1/2,0-1/6,0,7/12
-x+1/3,-x+y+2/3,-z+7/6 2[0,1,0]0,1/2,01/6,0,7/12
x-y+1/3,-y+2/3,-z+7/6 2[1,0,0]0,0,00,1/3,7/12
-x+1/3,-y+2/3,-z+2/3 -1--1/6,1/3,1/3
y+1/3,-x+y+2/3,-z+2/3 -3^1[0,0,1]0,0,02/3,1/3,1/3
x-y+1/3,x+2/3,-z+2/3 -3^-1[0,0,1]0,0,0-1/3,1/3,1/3
-y+1/3,-x+2/3,z+1/6 -2[1,1,0]-1/6,1/6,1/61/2,0,0
x+1/3,x-y+2/3,z+1/6 -2[0,1,0]1/3,1/6,1/6-1/2,0,0
-x+y+1/3,y+2/3,z+1/6 -2[1,0,0]1/3,2/3,1/60,0,0 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
f361x,y,z
e182x,0,1/4
d18-11/2,0,0
c1230,0,z
b6-30,0,0
a6320,0,1/4 

Harker planes:
Algebraic Normal vector A point in the plane
x-y,-x-2*y,0[0,0,1]0,0,0
x+y,-x-y,2*z+1/2[1,1,0]0,0,1/2
2*x,x,2*z+1/2[0,1,0]0,0,1/2
y,2*y,2*z+1/2[1,0,0]0,0,1/2 

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2

Grid factors implied by symmetries:
  Space group: (3, 3, 6)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  Euclidean normalizer: (3, 3, 6)

  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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