# Hollow cuboid cupoliprism

Hollow cuboid cupoliprism | |
---|---|

Rank | 4 |

Type | Scaliform |

Notation | |

Bowers style acronym | Hocucup |

Elements | |

Cells | 12 tetrahedra as 6 stella octangulae, 12 blends of 2 triangular prisms |

Faces | 48 triangles, 24 squares |

Edges | 24+48 |

Vertices | 24 |

Vertex figure | Faceted wedge, edge lengths 1 (equilateral triangles' edges), √2 (pseudo-edge), √2 (other edges) |

Measures (edge length 1) | |

Circumradius | |

Height | |

Related polytopes | |

Army | Cope |

Regiment | Hocucup |

Conjugate | None |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | No |

Nature | Tame |

The **hollow cubic cupoliprism** or **hocucup** is a prismatic scaliform polychoron that consists of 6 stella octangulae (or 12 tetrahedra) and 12 blends of 2 triangular prisms. Each vertex is met by two tetrahedra and four blends of 2 triangular prisms.

This polychoron can be created as a blend of 6 tetrahedral prisms (in the form of 6 digonal antiduoprisms). In the process all the tetrahedra compound in pairs, while the triangular prisms blend in pairs at a square face. The object has cube prismatic symmetry and has the vertices of a scaled cuboctahedral prism.

It was first discovered and described by Polytope Discord user _Geometer on November 20, 2020.

## Vertex coordinates[edit | edit source]

The vertices of a hollow cubic cupoliprism of edge length 1 are given by all permutations of the first three coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "Hocucup".
- Bowers, Jonathan. "Category S1: Simple Scaliforms" (#S6).