# Hexagonal trapezohedron

Hexagonal trapezohedron | |
---|---|

Type | trapezohedra |

Coxeter diagram | |

Faces | 12 kites |

Edges | 24 |

Vertices | 14 |

Face configuration | V6.3.3.3 |

Symmetry group | D_{6d}, [2^{+},12], (2*6), order 24 |

Rotation group | D_{6}, [2,12]^{+}, (66), order 12 |

Dual polyhedron | hexagonal antiprism |

Properties | convex, face-transitive |

The **hexagonal trapezohedron** or **deltohedron** is the fourth in an infinite series of face-uniform polyhedra which are dual polyhedron to the antiprisms. It has twelve faces which are congruent kites.

## Related polyhedra

Uniform hexagonal dihedral spherical polyhedra | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Symmetry: [6,2], (*622) | [6,2]^{+}, (622) |
[6,2^{+}], (2*3) | ||||||||||||

{6,2} | t{6,2} | r{6,2} | t{2,6} | {2,6} | rr{6,2} | tr{6,2} | sr{6,2} | s{2,6} | ||||||

Duals to uniforms | ||||||||||||||

V6^{2} |
V12^{2} |
V6^{2} |
V4.4.6 | V2^{6} |
V4.4.6 | V4.4.12 | V3.3.3.6 | V3.3.3.3 |

Family of trapezohedra V.n.3.3.3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Polyhedron | ||||||||||

Tiling | ||||||||||

Config. | V2.3.3.3 | V3.3.3.3 | V4.3.3.3 | V5.3.3.3 | V6.3.3.3 | V7.3.3.3 | V8.3.3.3 | ...V10.3.3.3 | ...V12.3.3.3 | ...V∞.3.3.3 |

## External links

- Virtual Reality Polyhedra The Encyclopedia of Polyhedra

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