# Rhombitetratetrahedron

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Rhombitetratetrahedron | |
---|---|

Rank | 3 |

Type | Semi-uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Ratet |

Coxeter diagram | x3o3y |

Elements | |

Faces | 4+4 triangles, 6 rectangles |

Edges | 12+12 |

Vertices | 12 |

Vertex figure | Isosceles trapezoid |

Measures (edge lengths a, b) | |

Circumradius | |

Volume | |

Dihedral angle | |

Central density | 1 |

Related polytopes | |

Army | Ratet |

Regiment | Ratet |

Dual | Deltoidal dodecahedron |

Conjugate | Rhombitetratetrahedron |

Abstract & topological properties | |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{3}, order 24 |

Convex | Yes |

Nature | Tame |

The **rhombitetratetrahedron**, or **ratet**, is a convex semi-uniform polyhedron that is a tetrahedral-symmetric variant of the cuboctahedron. It has 2 sets of 4 triangles of generally different sizes, with 6 rectangles connecting them. Half of the edges are of each size.

A rhombitetratetrahedron is the vertex figure of one uniform polychoron, the grand ditetrahedronary hexacosidishecatonicosachoron.

## Vertex coordinates[edit | edit source]

A rhombitetratetrahedron with edge lengths a and b has vertices given by all permutations and even sign changes of: