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Result of symbol lookup:
  Space group number: 111
  Schoenflies symbol: D2d^1
  Hermann-Mauguin symbol: P -4 2 m
  Hall symbol: P -4 2

Input space group symbol: P -4 2 m
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

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

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
o81x,y,z
n4mx,x,z
m420,1/2,z
l42x,1/2,0
k42x,0,1/2
j42x,1/2,1/2
i42x,0,0
h2mm21/2,1/2,z
g2mm20,0,z
f22221/2,0,1/2
e22221/2,0,0
d1-42m1/2,1/2,0
c1-42m0,0,1/2
b1-42m1/2,1/2,1/2
a1-42m0,0,0

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant 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)
  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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