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Result of symbol lookup:
Space group number: 115
Schoenflies symbol: D2d^5
HermannMauguin symbol: P 4 m 2
Hall symbol: P 4 2
Input space group symbol: P 4 m 2
Convention: Default
Number of lattice translations: 1
Space group is acentric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 8
Parallelepiped containing an asymmetric unit:
0<=x<=1/2; 0<=y<=1/2; 0<=z<=1/2
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

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

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

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

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

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

l  8  1  x,y,z

k  4  m  x,1/2,z

j  4  m  x,0,z

i  4  2  x,x,1/2

h  4  2  x,x,0

g  2  mm2  0,1/2,z

f  2  mm2  1/2,1/2,z

e  2  mm2  0,0,z

d  1  42m  0,0,1/2

c  1  42m  1/2,1/2,1/2

b  1  42m  1/2,1/2,0

a  1  42m  0,0,0

Harker planes:
Algebraic
 Normal vector
 A point in the plane

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

x+y,xy,2*z  [1,1,0]  0,0,0

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