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Result of symbol lookup:
  Space group number: 191
  Schoenflies symbol: D6h^1
  Hermann-Mauguin symbol: P 6/m m m
  Hall symbol: -P 6 2

Input space group symbol: P 6/m m 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<=1/2; -1/3<=y<=0; 0<=z<=1/2

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

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
r241x,y,z
q12mx,y,1/2
p12mx,y,0
o12mx,2*x,z
n12mx,0,z
m6mm2x,2*x,1/2
l6mm2x,2*x,0
k6mm2x,0,1/2
j6mm2x,0,0
i6mm21/2,0,z
h43m1/3,-1/3,z
g3mmm1/2,0,1/2
f3mmm1/2,0,0
e26mm0,0,z
d2-62m1/3,-1/3,1/2
c2-62m1/3,-1/3,0
b16/mmm0,0,1/2
a16/mmm0,0,0

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

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, 1)
  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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