Polyhedral group

It has been suggested that this article or section be merged into Point groups in three dimensions. (Discuss) Proposed since February 2010.

Td, [3,3], *332	Oh, [4,3], *432	Ih, [5,3], *532
T, [3,3]+, 332	O, [4,3]+, 432	I, [5,3]+, 532
Tetrahedral group Order 12 (24)	Octahedral group Order 24 (48)	Icosahedral group Order 60 (120)

In geometry, the polyhedral group is any of the symmetry groups of the Platonic solids. There are three polyhedral groups:

• The tetrahedral group of order 12, rotational symmetry group of the regular tetrahedron.
• The octahedral group of order 24, rotational symmetry group of the cube and the regular octahedron.
• The icosahedral group of order 60, rotational symmetry group of the regular dodecahedron and the regular icosahedron.

These symmetries double to 24, 48, 120 respectly for the full reflectional groups.

See also

• Wythoff symbol
• List of spherical symmetry groups‎

References

• Coxeter, H. S. M. Regular Polytopes, 3rd ed. New York: Dover, 1973. (The Polyhedral Groups. §3.5, pp. 46–47)

External links

• Weisstein, Eric W., "PolyhedralGroup" from MathWorld.