Chiral dodecahedral symmetry

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

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.

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)