# Chiral dodecahedral symmetry

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Chiral dodecahedral symmetry | |
---|---|

Rank | 3 |

Space | Spherical |

Order | 60 |

Elements | |

Axes | 6 × (H_{2}×A_{1})+, 10 × (A_{2}×A_{1})/2, 15 × K_{3}+ |

**Chiral icosahedral symmetry**, also known as **chiral dodecahedral symmetry**, **kidoic symmetry**, and notated as **H _{3}+**, 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[edit | edit source]

- A
_{3}+ (maximal) - (H
_{2}×A_{1})+ (maximal) - H
_{2}+×I - (A
_{2}×A_{1})+ (maximal) - A
_{2}+×I - K
_{3}+ - K
_{2}+×I - I×I×I

### Convex polytopes with H_{3}+ symmetry[edit | edit source]

- 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)