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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
f181x,y,z
e9-11/2,0,0
d9-11/2,0,1/2
c630,0,z
b3-30,0,1/2
a3-30,0,0
```
Harker planes:
```
Algebraic Normal vector A point in the plane
x-y,-x-2*y,0[0,0,1]0,0,0
```
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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