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+
 * A3+×2
 * A3+
 * I2(10)×A1/2
 * I2(10)+×A1/2
 * G2×A1/2
 * G2+×A1/2
 * H2×A1+
 * H2×I
 * H2+×I
 * A2×A1+
 * A2×I
 * A2+×I
 * A1×A1×A1
 * A1×A1×A1+
 * A1×A1×I
 * A1×A1+×A1
 * A1×A1+×I
 * A1×A1+×A1/2
 * 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)