# Triangular retroprism

Triangular retroprism | |
---|---|

Rank | 3 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Trirp |

Elements | |

Faces | 6 isosceles triangles, 2 triangles |

Edges | 6+6 |

Vertices | 6 |

Vertex figure | Bowtie |

Measures (edge lengths 1 (base), a (sides)) | |

Circumradius | |

Volume | |

Height | |

Related polytopes | |

Army | Trip |

Regiment | Trirp |

Dual | Triangular concave antitegum |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{2}×A_{1}, order 12 |

Convex | No |

Nature | Tame |

The **triangular retroprism** or **trirp**, also called the **triangular crossed antiprism**, is a prismatic isogonal polyhedron. It consists of 2 base triangles and 6 side triangles. The side triangles are isosceles triangles. Each vertex joins one base triangle and three side triangles. It is a crossed antiprism based on a triangle, seen as a 3/2-gon rather than 3/1.

It cannot be made uniform, because if all the edges are of the same length, the height becomes zero and all of the triangles coincide. It can be thought of as a degenerate uniform polyhedron.

It is isomorphic to the octahedron.

## In vertex figures[edit | edit source]

Triangular retroprisms occur as vertex figures of seven nonconvex uniform polychora: the faceted rectified pentachoron, faceted rectified tesseract, faceted rectified icositetrachoron, faceted rectified hecatonicosachoron, faceted rectified small stellated hecatonicosachoron, faceted rectified great grand hecatonicosachoron, and faceted rectified great grand stellated hecatonicosachoron.

## External links[edit | edit source]

- Klitzing, Richard. "trirp".