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Result of symbol lookup:
  Space group number: 148
  Schoenflies symbol: C3i^2
  Hermann-Mauguin symbol: R -3
  Trigonal using hexagonal axes
  Hall symbol: -R 3

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

Number of lattice translations: 3
Space group is centric.
Number of representative symmetry operations: 3
Total number of symmetry operations: 18

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

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
-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
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
-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
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
-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

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator

Harker planes:
Algebraic Normal vector A point in the plane

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2
  Further generators:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
-y,-x,z -2[1,1,0]0,0,00,0,0

Grid factors implied by symmetries:
  Space group: (3, 3, 3)
  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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