Symmetry group (InstanceClass, 3)

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Revision as of 23:10, 23 March 2014

WIP

The following table contains all the symmetry groups used by CRF polyhedra:

n =	2	3	4	5
special	C_s Plane
C_n Chiral axial				C₅ Chiral rhodoaxial
C_nv Axial	C_2v Biaxial (biplane)	C_3v Pyroaxial	C_4v Stauroaxial	C_5v Rhodoaxial
D_n Chiral antiprismatic		D₃ Chiral pyroantiprismatic	D₄ Chiral stauroantiprismatic	D₅ Chiral rhodoantiprismatic
D_nd Antiprismatic	D_2d Biantiprismatic	D_3d Pyroantiprismatic	D_4d Stauroantiprismatic	D_5d Rhodoantiprismatic
D_nh Prismatic	D_2h Biprismatic (triplane, brick)	D_3h Pyroprismatic	D_4h Stauroprismatic	D_5h Rhodoprismatic
Chiral polyhedral			O Chiral staurohedral	I Chiral rhodohedral
Polyhedral		T_d Pyrohedral	O_h Staurohedral	I_h Rhodohedral

There are five more 3D symmetry groups, which are not seen in CRF polyhedra: C₁ (asymmetry), C_nh (cyclic prismatic symmetry), S_n (S₂ being point symmetry), T (chiral pyrohedral symmetry) and T_h (pyritohedral symmetry).

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-	There are five more 3D symmetry groups, which are not seen in CRF polyhedra: C<sub>1</sub> ([[asymmetry]]), C<sub>''n''h</sub> ([[cyclic prismatic symmetry]]), S<sub>''n''</sub> (S<sub>2</sub> being [[point symmetry]]), T ([[chiral pyrohedral symmetry]]), T<sub>h</sub> ([[pyritohedral symmetry]])	+	There are five more 3D symmetry groups, which are not seen in CRF polyhedra: C<sub>1</sub> ([[asymmetry]]), C<sub>''n''h</sub> ([[cyclic prismatic symmetry]]), S<sub>''n''</sub> (S<sub>2</sub> being [[point symmetry]]), T ([[chiral pyrohedral symmetry]]) and T<sub>h</sub> ([[pyritohedral symmetry]]).