Dodecahedral symmetry

H3, also known as doic symmetry, dodecahedral symmetry, or icosahedral symmetry, is a 3D spherical Coxeter group. It is the symmetry group of the dodecahedron and icosahedron.

Subgroups

 * H3+ (maximal)
 * A3+×2 (maximal)
 * A3+
 * (I2(10)×A1)/2 (maximal)
 * (I2(10)+×A1)/2
 * (G2×A1)/2 (maximal)
 * (G2+×A1)/2
 * (H2×A1)+
 * H2×I
 * H2+×I
 * (A2×A1)+
 * A2×I
 * A2+×I
 * K3
 * K3+
 * K2×I
 * K2+×A1
 * K2+×I
 * ±(I×I×I)
 * A1×I×I
 * I×I×I

Convex polytopes with H3 symmetry

 * Dodecahedron (regular)/Icosahedron (regular)
 * Icosidodecahedron (isogonal)/Rhombic triacontahedron (isotopic)
 * Truncated dodecahedron (isogonal)/Triakis icosahedron (isotopic)
 * Truncated icosahedron (isogonal)/Pentakis dodecahedron (isotopic)
 * Small rhombicosidodecahedron (isogonal)/Deltoidal hexecontahedron (isotopic)
 * Great rhombicosidodecahedron (isogonal)/Disdyakis triacontahedron (isotopic)