[Index of services]
[New input]
Result of symbol lookup:
Space group number: 187
Schoenflies symbol: D3h^1
HermannMauguin symbol: P 6 m 2
Hall symbol: P 6 2
Input space group symbol: P 6 m 2
Convention: Default
Number of lattice translations: 1
Space group is acentric.
Number of representative symmetry operations: 12
Total number of symmetry operations: 12
Parallelepiped containing an asymmetric unit:
0<=x<=2/3; 0<=y<=2/3; 0<=z<=1/2
List of symmetry operations:
Matrix
 Rotationpart type
 Axis direction
 Screw/glide component
 Origin shift

x,y,z
 1      

x+y,x,z
 6^1  [0,0,1]  0,0,0  0,0,0

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

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

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

y,xy,z
 6^1  [0,0,1]  0,0,0  0,0,0

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

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

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

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

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

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

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

o  12  1  x,y,z

n  6  m  x,x,z

m  6  m  x,y,1/2

l  6  m  x,y,0

k  3  mm2  x,x,1/2

j  3  mm2  x,x,0

i  2  3m  1/3,1/3,z

h  2  3m  1/3,1/3,z

g  2  3m  0,0,z

f  1  62m  1/3,1/3,1/2

e  1  62m  1/3,1/3,0

d  1  62m  1/3,1/3,1/2

c  1  62m  1/3,1/3,0

b  1  62m  0,0,1/2

a  1  62m  0,0,0

Harker planes:
Algebraic
 Normal vector
 A point in the plane

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

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

0,x2*y,2*z  [2,1,0]  0,0,0

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

Additional generators of Euclidean normalizer:
Number of structureseminvariant vectors and moduli: 1
Vector Modulus
(2, 4, 3) 6
Inversion through a centre at: 0,0,0
Grid factors implied by symmetries:
Space group: (1, 1, 1)
Structureseminvariant vectors and moduli: (3, 3, 2)
Euclidean normalizer: (3, 3, 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]