# Chiral tetrahedral symmetry

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### Convex polytopes with A

Chiral tetrahedral symmetry | |
---|---|

Rank | 3 |

Space | Spherical |

Order | 12 |

Elements | |

Axes | 3 × A_{1}×A_{1}×A_{1}+, 4 × A_{2}+×I |

**Chiral tetrahedral symmetry**, also known as **kitettic symmetry** and notated **A _{3}+** is a 3D spherical symmetry group. It is the symmetry group of the tetrahedron with all the reflections removed.

### Subgroups[edit | edit source]

- Chiral triangular pyramidal symmetry (maximal)
- Chiral digonal prismatic symmetry (maximal)
- Chiral digonal pyramidal symmetry
- Identity symmetry

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

- Tetrahedron (regular)
- Tetratetrahedron (isogonal)/Triangular antitegum (isotopic)
- Truncated tetrahedron (isogonal)/Triakis tetrahedron (isotopic)
- Rhombitetratetrahedron (isogonal)/Deltoidal dodecahedron (isotopic)
- Snub tetrahedron (isogonal)/Tetartoid (isotopic)