# Triangular cupolic prism

Triangular cupolic prism | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Tricupe |

Coxeter diagram | xx ox3xx&#x |

Elements | |

Cells | 1+3 triangular prisms, 3 cubes, 2 triangular cupolas, 1 hexagonal prism |

Faces | 2+6 triangles, 3+3+3+6+6 squares, 2 hexagons |

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

Vertices | 6+12 |

Vertex figures | 6 rectangular pyramids, base edge lengths 1 and √2, side edge length √2 |

12 irregular tetrahedra, edge lengths 1 (1), √2 (4), and √3 (1) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–cube: |

Tricu–3–trip: 90° | |

Tricu–4–cube: 90° | |

Tricu–6–hip: 90° | |

Trip–4–hip: | |

Cube–4–hip: | |

Heights | Tricu atop tricu: 1 |

Trip atop hip: | |

Central density | 1 |

Related polytopes | |

Army | Tricupe |

Regiment | Tricupe |

Dual | Semibisected hexagonal trapezohedral tegum |

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 cupolic prism**, or **tricupe**, is a CRF segmentochoron (designated K-4.45 on Richard Klitzing's list). It consists of 2 triangular cupolas, 4 triangular prisms, 3 cubes, and 1 hexagonal prism.

As the name suggests, it is a prism based on the triangular cupola. As such, it is a segmentochoron between two triangular cupolas. It can also be viewed as a segmentochoron between a hexagonal prism and a triangular prism.

Two triangular cupolic prisms can be joined at their hexagonal prismatic cells in opposite orientations to form a cuboctahedral prism. By rotating one of the triangular cupolic prisms before joining, one can instead form a triangular orthobicupolic prism.

## Vertex coordinates[edit | edit source]

Coordinates of the vertices of a triangular cupolic prism of edge length 1 centered at the origin are given by:

## External links[edit | edit source]

- Klitzing, Richard. "tricupe".