Chiral dodecahedral symmetry

Chiral icosahedral symmetry, also known as chiral dodecahedral symmetry, kidoic symmetry, and notated as H₃+, is a 3D spherical symmetry 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.

Chiral dodecahedral symmetry
Rank	3
Space	Spherical
Order	60
Elements
Axes	6 × (H2×A1)+, 10 × (A2×A1)/2, 15 × K3+

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)