Symmetry group (InstanceClass, 3)

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WIP

Three dimensions

2	3	4	5
C_s Plane
			C₅ Chiral rhodoaxial
C_2v Biaxial	C_3v Pyroaxial	C_4v Stauroaxial	C_5v Rhodoaxial
	D₃ Chiral pyroantiprismatic	D₄ Chiral stauroantiprismatic	D₅ Chiral rhodoantiprismatic
D_2d Biantiprismatic	D_3d Pyroantiprismatic	D_4d Stauroantiprismatic	D_5d Rhodoantiprismatic
D_2h Biprismatic (brick)	D_3h Pyroprismatic	D_4h Stauroprismatic	D_5h Rhodoprismatic
		O Chiral staurohedral	I Chiral rhodohedral
	T_d Pyrohedral	O_h Staurohedral	I_h Rhodohedral

Five symmetry groups are not seen in CRF polyhedra: C₁ (asymmetry), C_nh (chiral prismatic symmetry), S_n (S₂ being point symmetry), T (chiral pyrohedral symmetry), T_h (pyritohedral symmetry)