Tetrahedral symmetry

A3, also known as tettic symmetry or tetrahedral symmetry, is a 3D spherical Coxeter group. It is the symmetry group of the regular tetrahedron.

Subgroups

 * A3+ (maximal)
 * (BC2×A1)/2 (maximal)
 * (BC2+×A1)/2
 * A2×I (maximal)
 * A2+×I
 * K3+
 * K2×I
 * K2+×I
 * A1×I×I
 * I×I×I

Convex polytopes with A3 symmetry

 * Tetrahedron (regular)
 * Tetratetrahedron (isogonal)/Rhombic hexahedron (isotopic)
 * Truncated tetrahedron (isogonal)/Triakis tetrahedron (isotopic)
 * Rhombitetratetrahedron (isogonal)/Deltoidal dodecahedron (isotopic)
 * Great rhombitetratetrahedron (isogonal)/Disdyakis hexahedron (isotopic)