[Index of services] [New input]
```Result of symbol lookup:
Space group number: 81
Schoenflies symbol: S4^1
Hermann-Mauguin symbol: P -4
Hall symbol: P -4

Input space group symbol: P -4
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Number of representative symmetry operations: 4
Total number of symmetry operations: 4

Parallelepiped containing an asymmetric unit:
0<=x<=1/2; 0<=y<=1/2; 0<=z<1

List of symmetry operations:
```
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
y,-x,-z -4^1[0,0,1]0,0,00,0,0
-x,-y,z 2[0,0,1]0,0,00,0,0
-y,x,-z -4^-1[0,0,1]0,0,00,0,0
```
List of Wyckoff positions:
```
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
h41x,y,z
g220,1/2,z
f221/2,1/2,z
e220,0,z
d1-41/2,1/2,1/2
c1-41/2,1/2,0
b1-40,0,1/2
a1-40,0,0
```
Harker planes:
```
Algebraic Normal vector A point in the plane
2*x,2*y,0[0,0,1]0,0,0
```
Additional generators of Euclidean normalizer:
Number of structure-seminvariant vectors and moduli: 2
Vector    Modulus
(0, 0, 1) 2
(1, 1, 0) 2
Inversion through a centre at: 0,0,0
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: (1, 1, 1)
Structure-seminvariant vectors and moduli: (2, 2, 2)
Euclidean normalizer: (2, 2, 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]