# Triangular cupofastegium

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Triangular cupofastegium | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Tricuf |

Coxeter diagram | ox xx3xo&#x |

Elements | |

Cells | 3 tetrahedra, 1+3 triangular prisms, 2 triangular cupolas |

Faces | 2+6+6 triangles, 3+6 squares, 1 hexagon |

Edges | 3+3+3+6+12 |

Vertices | 6+6 |

Vertex figures | 6 skewed rectangular pyramids, base edge lengths 1, √2, 1, √2, side edge lengths 1, 1, √2. √2 |

6 sphenoids, edge lengths 1 (3), √2 (2), and √3 (1) | |

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angles | Trip–4–trip: |

Tet–3–trip: | |

Tet–3–tricu: | |

Tricu–6–tricu: | |

Tricu–4–trip: | |

Tricu–3–trip: | |

Heights | Trig atop tricu: |

Trip atop hig: | |

Central density | 1 |

Related polytopes | |

Army | Tricuf |

Regiment | Tricuf |

Dual | Triangular cupolanotch |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{2}×A_{1}×I, order 12 |

Convex | Yes |

Nature | Tame |

The **triangular cupofastegium**, or **tricuf**, also called the **triangular orthobicupolic ring**, is a CRF segmentochoron (designated K-4.25 on Richard Klitzing's list). It consists of 1+3 triangular prisms, 3 tetrahedra, and 2 triangular cupolas.

The triangular cupofastegium can be thought of as a wedge of the small prismatodecachoron, or as a part of the larger segmentochoron tetrahedron atop cuboctahedron, with the remainder forming the segmentochoron tetrahedron atop triangular cupola.

## Vertex coordinates[edit | edit source]

The vertices of a triangular cupofastegium with edge length 1 are given by:

## Representations[edit | edit source]

A triangular cupofastegium has the following Coxeter diagrams:

- ox xx3xo&#x (full symmetry)
- xxx3oxo&#x (A2 symmetry only, seen with triangle atop triangular cupola)

## External links[edit | edit source]

- Klitzing, Richard. "tricuf".