# Tetrahedron atop triangular cupola

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Tetrahedron atop triangular cupola | |
---|---|

Rank | 4 |

Type | Segmentotope |

Space | Spherical |

Notation | |

Bowers style acronym | Tetatricu |

Coxeter diagram | ooxx3oxxo&#xr |

Elements | |

Cells | 2 tetrahedra, 6 triangular prisms, 2 triangular cupolax |

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

Edges | 6+6+6+12 |

Vertices | 1+6+6 |

Vertex figures | 1 triangular antiprism, edge lengths 1 (base) and √2 (sides) |

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

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

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angles | Trip-4-trip: |

Tet-3-trip: | |

Tricu-6-tricu: | |

Tet-3-tricu: | |

Trip-4-tricu: | |

trip-3-tricu: | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Tetatricu |

Regiment | Tetatricu |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (G_{2}×A_{1})/2×I, order 12 |

Convex | Yes |

Nature | Tame |

**Tetrahedron atop triangular cupola**, or **tetatricu**, is a CRF segmentochoron (designated K-4.24 on Richard Klitzing's list). As the name suggests, it consists of a tetrahedron and a triangular cupola as bases, connected by 1 additional tetrahedron, 1 additional triangular cupola, and 6 triangular prisms.

It can be formed by diminishing a tetrahedron atop cuboctahedron segmentochoron by a triangular cupofastegium, leaving a further triangular cupola behind while removing several tetrahedral and triangular prism cells. Therefore, its vertices are a subset of those of the uniform small prismatodecachoron.

## Vertex coordinates[edit | edit source]

The vertices of a tetrahedron atop triangular cupola segmentochoron of edge length 1 are given by:

- ,
- ,
- ,
- ,
- ,
- ,
- .

## External links[edit | edit source]

- Klitzing, Richard. "tetatricu".