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Result of symbol lookup:
  Space group number: 137
  Schoenflies symbol: D4h^15
  Hermann-Mauguin symbol: P 42/n m c
  Origin choice: 2
  Hall symbol: -P 4ac 2a

Input space group symbol: P 42/n m c :2
Convention: Default

Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 16

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

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y+1/2,x,z+1/2 4^1[0,0,1]0,0,1/21/4,1/4,0
-x+1/2,-y+1/2,z 2[0,0,1]0,0,01/4,1/4,0
y,-x+1/2,z+1/2 4^-1[0,0,1]0,0,1/21/4,1/4,0
x+1/2,-y,-z 2[1,0,0]1/2,0,00,0,0
y+1/2,x+1/2,-z+1/2 2[1,1,0]1/2,1/2,00,0,1/4
-x,y+1/2,-z 2[0,1,0]0,1/2,00,0,0
-y,-x,-z+1/2 2[-1,1,0]0,0,00,0,1/4
-x,-y,-z -1--0,0,0
y-1/2,-x,-z-1/2 -4^1[0,0,1]0,0,0-1/4,1/4,-1/4
x-1/2,y-1/2,-z -2[0,0,1]-1/2,-1/2,00,0,0
-y,x-1/2,-z-1/2 -4^-1[0,0,1]0,0,01/4,-1/4,-1/4
-x-1/2,y,z -2[1,0,0]0,0,0-1/4,0,0
-y-1/2,-x-1/2,z-1/2 -2[1,1,0]0,0,-1/2-1/2,0,0
x,-y-1/2,z -2[0,1,0]0,0,00,-1/4,0
y,x,z-1/2 -2[-1,1,0]0,0,-1/20,0,0

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
h161x,y,z
g8m1/4,y,z
f82x,-x,1/4
e8-10,0,0
d4mm21/4,1/4,z
c4mm2-1/4,1/4,z
b2-42m-1/4,1/4,1/4
a2-42m-1/4,1/4,-1/4

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

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

Grid factors implied by symmetries:
  Space group: (2, 2, 2)
  Structure-seminvariant 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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