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Result of symbol lookup:
  Space group number: 193
  Schoenflies symbol: D6h^3
  Hermann-Mauguin symbol: P 63/m c m
  Hall symbol: -P 6c 2

Input space group symbol: P 63/m c m
Convention: Default

Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 12
Total number of symmetry operations: 24

Parallelepiped containing an asymmetric unit:
  0<=x<=2/3; 0<=y<=1/3; 0<=z<=1/4

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
x-y,x,z+1/2 6^1[0,0,1]0,0,1/20,0,0
-y,x-y,z 3^1[0,0,1]0,0,00,0,0
-x,-y,z+1/2 2[0,0,1]0,0,1/20,0,0
-x+y,-x,z 3^-1[0,0,1]0,0,00,0,0
y,-x+y,z+1/2 6^-1[0,0,1]0,0,1/20,0,0
-y,-x,-z 2[-1,1,0]0,0,00,0,0
x-y,-y,-z+1/2 2[1,0,0]0,0,00,0,1/4
x,x-y,-z 2[2,1,0]0,0,00,0,0
y,x,-z+1/2 2[1,1,0]0,0,00,0,1/4
-x+y,y,-z 2[1,2,0]0,0,00,0,0
-x,-x+y,-z+1/2 2[0,1,0]0,0,00,0,1/4
-x,-y,-z -1--0,0,0
-x+y,-x,-z-1/2 -6^1[0,0,1]0,0,00,0,-1/4
y,-x+y,-z -3^1[0,0,1]0,0,00,0,0
x,y,-z-1/2 -2[0,0,1]0,0,00,0,-1/4
x-y,x,-z -3^-1[0,0,1]0,0,00,0,0
-y,x-y,-z-1/2 -6^-1[0,0,1]0,0,00,0,-1/4
y,x,z -2[-1,1,0]0,0,00,0,0
-x+y,y,z-1/2 -2[1,0,0]0,0,-1/20,0,0
-x,-x+y,z -2[2,1,0]0,0,00,0,0
-y,-x,z-1/2 -2[1,1,0]0,0,-1/20,0,0
x-y,-y,z -2[1,2,0]0,0,00,0,0
x,x-y,z-1/2 -2[0,1,0]0,0,-1/20,0,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
l241x,y,z
k12mx,0,z
j12mx,y,1/4
i122x,2*x,0
h831/3,-1/3,z
g6mm2x,0,1/4
f62/m1/2,0,0
e43m0,0,z
d4321/3,-1/3,0
c4-61/3,-1/3,1/4
b2-3m0,0,0
a2-62m0,0,1/4

Harker planes:
Algebraic Normal vector A point in the plane
-y,-x-y,1/2[0,0,1]0,0,1/2
x-y,-x-2*y,0[0,0,1]0,0,0
x+y,x+y,2*z[-1,1,0]0,0,0
y,2*y,2*z+1/2[1,0,0]0,0,1/2
0,x-2*y,2*z[2,1,0]0,0,0
x+y,-x-y,2*z+1/2[1,1,0]0,0,1/2
2*x+y,0,2*z[1,2,0]0,0,0
2*x,x,2*z+1/2[0,1,0]0,0,1/2

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2

Grid factors implied by symmetries:
  Space group: (1, 1, 2)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  Euclidean normalizer: (1, 1, 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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