Chiral dodecahedral symmetry

Chiral icosahedral symmetry, also known as chiral dodecahedral symmetry, kidoic symmetry, and notated as H3+, is a 3D spherical Coxeter group. It is the symmetry group of the snub dodecahedron, or equivalently the symmetry group of the dodecahedron and icosahedron with all the reflections removed.

Subgroups

 * A3+ (maximal)
 * (H2×A1)+ (maximal)
 * H2+×I
 * (A2×A1)+ (maximal)
 * A2+×I
 * K3+
 * K2+×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)
 * Snub dodecahedron (isogonal)/Pentagonal hexecontahedron (isotopic)