# Pentagonal-cubic duoprism

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Pentagonal-cubic duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Pecube |

Coxeter diagram | x5o x4o3o |

Elements | |

Tera | 5 tesseracts, 6 square-pentagonal duoprisms |

Cells | 5+30 cubes, 12 pentagonal prisms |

Faces | 30+60 squares, 8 pentagons |

Edges | 40+60 |

Vertices | 40 |

Vertex figure | Triangular scalene, edge lengths (1+√5)/2 (top), √2 (base triangle and sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tes–cube–tes: 108° |

Tes–cube–squipdip: 90° | |

Squipdip–pip–squipdip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 11 |

Level of complexity | 10 |

Related polytopes | |

Army | Pecube |

Regiment | Pecube |

Dual | Pentagonal-octahedral duotegum |

Conjugate | Pentagrammic-cubic duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×H_{2}, order 480 |

Convex | Yes |

Nature | Tame |

The **pentagonal-cubic duoprism** or **pecube**, also known as a **square-pentagonal duoprismatic prism**, is a convex uniform duoprism that consists of 5 tesseracts and 6 square-pentagonal duoprisms. Each vertex joins 2 tesseracts and 3 square-pentagonal duoprisms. It is a duoprism based on a square and a pentagonal prism, which makes it a convex segmentoteron.

## Vertex coordinates[edit | edit source]

The vertices of a pentagonal-cubic duoprism of edge length 1 are given by:

## Representations[edit | edit source]

A pentagonal-cubic duoprism has the following Coxeter diagrams:

- x5o x4o3o (full symmetry)
- x x4o x5o (square-pentagonal duoprismatic prism)
- x x x x5o (pentagonal prismatic prismatic prism)

## External links[edit | edit source]

- Klitzing, Richard. "pecube".