# Pentagonal-cuboctahedral duoprism

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Pentagonal-cuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Peco |

Coxeter diagram | x5o o4x3o |

Elements | |

Tera | 8 triangular-pentagonal duoprisms, 6 square-pentagonal duoprisms, 5 cuboctahedral prisms |

Cells | 40 triangular prisms, 30 cubes, 24 pentagonal prisms, 5 cuboctahedra |

Faces | 40 triangles, 30+120 squares, 12 pentagons |

Edges | 60+120 |

Vertices | 60 |

Vertex figure | Rectangular scalene, edge lengths 1, √2, 1, √2 (base rectangle), (1+√5)/2 (top), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Trapedip–pip–squipdip: |

Cope–co–cope: 108° | |

Trapedip–trip–cope: 90° | |

Squipdip–cube–cope: 90° | |

Central density | 1 |

Number of external pieces | 19 |

Level of complexity | 20 |

Related polytopes | |

Army | Peco |

Regiment | Peco |

Dual | Pentagonal-rhombic dodecahedral duotegum |

Conjugate | Pentagrammic-cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×H_{2}, order 480 |

Convex | Yes |

Nature | Tame |

The **pentagonal-cuboctahedral duoprism** or **peco** is a convex uniform duoprism that consists of 5 cuboctahedral prisms, 6 square-pentagonal duoprisms, and 8 triangular-pentagonal duoprisms. Each vertex joins 2 cuboctahedral prisms, 2 triangular-pentagonal duoprisms, and 2 square-pentagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a pentagonal-cuboctahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "peco".