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Result of symbol lookup:
Space group number: 24
Schoenflies symbol: D2^9
HermannMauguin symbol: I 21 21 21
Hall symbol: I 2b 2c
Input space group symbol: I 21 21 21
Convention: Default
Number of lattice translations: 2
Space group is acentric.
Space group is chiral.
Number of representative symmetry operations: 4
Total number of symmetry operations: 8
Parallelepiped containing an asymmetric unit:
0<=x<=1/4; 0<=y<=1/2; 0<=z<1
List of symmetry operations:
Matrix
 Rotationpart type
 Axis direction
 Screw/glide component
 Origin shift

x,y,z
 1      

x,y+1/2,z
 2  [0,0,1]  0,0,0  0,1/4,0

x,y,z+1/2
 2  [1,0,0]  0,0,0  0,0,1/4

x,y+1/2,z+1/2
 2  [0,1,0]  0,1/2,0  0,0,1/4

x+1/2,y+1/2,z+1/2
 1      

x+1/2,y+1,z+1/2
 2  [0,0,1]  0,0,1/2  1/4,1/2,0

x+1/2,y+1/2,z+1
 2  [1,0,0]  1/2,0,0  0,1/4,1/2

x+1/2,y+1,z+1
 2  [0,1,0]  0,1,0  1/4,0,1/2

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

d  8  1  x,y,z

c  4  2  0,1/4,z

b  4  2  1/4,y,0

a  4  2  x,0,1/4

Harker planes:
Algebraic
 Normal vector
 A point in the plane

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

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

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

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