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Result of symbol lookup:
Space group number: 148
Schoenflies symbol: C3i^2
HermannMauguin 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
 Rotationpart type
 Axis direction
 Screw/glide component
 Origin shift

x,y,z
 1      

y,xy,z
 3^1  [0,0,1]  0,0,0  0,0,0

x+y,x,z
 3^1  [0,0,1]  0,0,0  0,0,0

x,y,z
 1      0,0,0

y,x+y,z
 3^1  [0,0,1]  0,0,0  0,0,0

xy,x,z
 3^1  [0,0,1]  0,0,0  0,0,0

x+2/3,y+1/3,z+1/3
 1      

y+2/3,xy+1/3,z+1/3
 3^1  [0,0,1]  0,0,1/3  1/3,1/3,0

x+y+2/3,x+1/3,z+1/3
 3^1  [0,0,1]  0,0,1/3  1/3,0,0

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]  0,0,0  1/3,1/3,1/6

xy+2/3,x+1/3,z+1/3
 3^1  [0,0,1]  0,0,0  1/3,2/3,1/6

x+1/3,y+2/3,z+2/3
 1      

y+1/3,xy+2/3,z+2/3
 3^1  [0,0,1]  0,0,2/3  0,1/3,0

x+y+1/3,x+2/3,z+2/3
 3^1  [0,0,1]  0,0,2/3  1/3,1/3,0

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]  0,0,0  2/3,1/3,1/3

xy+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

f  18  1  x,y,z

e  9  1  1/2,0,0

d  9  1  1/2,0,1/2

c  6  3  0,0,z

b  3  3  0,0,1/2

a  3  3  0,0,0

Harker planes:
Algebraic
 Normal vector
 A point in the plane

xy,x2*y,0  [0,0,1]  0,0,0

Additional generators of Euclidean normalizer:
Number of structureseminvariant vectors and moduli: 1
Vector Modulus
(0, 0, 1) 2
Further generators:
Matrix
 Rotationpart type
 Axis direction
 Screw/glide component
 Origin shift

y,x,z
 2  [1,1,0]  0,0,0  0,0,0

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