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Result of symbol lookup:
Space group number: 81
Schoenflies symbol: S4^1
HermannMauguin 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
 Rotationpart type
 Axis direction
 Screw/glide component
 Origin shift

x,y,z
 1      

y,x,z
 4^1  [0,0,1]  0,0,0  0,0,0

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

y,x,z
 4^1  [0,0,1]  0,0,0  0,0,0

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

h  4  1  x,y,z

g  2  2  0,1/2,z

f  2  2  1/2,1/2,z

e  2  2  0,0,z

d  1  4  1/2,1/2,1/2

c  1  4  1/2,1/2,0

b  1  4  0,0,1/2

a  1  4  0,0,0

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 structureseminvariant 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
 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: (1, 1, 1)
Structureseminvariant 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.
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