Symmetry group (InstanceClass, 3)

From Hi.gher. Space

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Three dimensions

The following table contains all the symmetry groups used by CRF polyhedra. The order of each group is given after an asterisk:

n = 2345

special
Cs *2
Plane
Cn *n
Chiral axial
C5 *5
Chiral rhodoaxial
Cnv *2n
Axial
C2v *4
Biaxial (biplane)
C3v *6
Pyroaxial
C4v *8
Stauroaxial
C5v *10
Rhodoaxial
Dn *2n
Chiral antiprismatic
D3 *6
Chiral pyroantiprismatic
D4 *8
Chiral stauroantiprismatic
D5 *10
Chiral rhodoantiprismatic
Dnd *4n
Antiprismatic
D2d *8
Biantiprismatic
D3d *12
Pyroantiprismatic
D4d *16
Stauroantiprismatic
D5d *20
Rhodoantiprismatic
Dnh *4n
Prismatic
D2h *8
Biprismatic (triplane, brick)
D3h *12
Pyroprismatic
D4h *16
Stauroprismatic
D5h *20
Rhodoprismatic

Chiral polyhedral
O *24
Chiral staurohedral
I *60
Chiral rhodohedral

Polyhedral
Td *24
Pyrohedral
Oh *48
Staurohedral
Ih *120
Rhodohedral

There are five more 3D symmetry groups, which are not seen in CRF polyhedra:

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