# Pentagonal-great rhombicuboctahedral duoprism

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Pentagonal-great rhombicuboctahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Pegirco |

Coxeter diagram | x5o x4x3x () |

Elements | |

Tera | 12 square-pentagonal duoprisms, 8 pentagonal-hexagonal duoprisms, 6 pentagonal-octagonal duoprisms, 5 great rhombicuboctahedral prisms |

Cells | 60 cubes, 24+24+24 pentagonal prisms, 40 hexagonal prisms, 30 octagonal prisms, 5 great rhombicuboctahedra |

Faces | 60+120+120+120 squares, 48 pentagons, 40 hexagons, 30 octagons |

Edges | 120+120+120+240 |

Vertices | 240 |

Vertex figure | Mirror-symmetric pentachoron, edge lengths √2, √3, √2+√2 (base triangle), (1+√5)/2 (top edge), √2 (side edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squipdip–pip–phiddip: |

Squipdip–pip–podip: 135° | |

Phiddip–pip–podip: | |

Gircope–girco–gircope: 108° | |

Squipdip–cube–gircope: 90° | |

Phiddip–hip–gircope: 90° | |

Podip–op–gircope: 90° | |

Central density | 1 |

Number of external pieces | 31 |

Level of complexity | 60 |

Related polytopes | |

Army | Pegirco |

Regiment | Pegirco |

Dual | Pentagonal-disdyakis dodecahedral duotegum |

Conjugates | Pentagrammic-great rhombicuboctahedral duoprism, Pentagonal-quasitruncated cuboctahedral duoprism, Pentagrammic-quasitruncated cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×H_{2}, order 480 |

Convex | Yes |

Nature | Tame |

The **pentagonal-great rhombicuboctahedral duoprism** or **pegirco** is a convex uniform duoprism that consists of 5 great rhombicuboctahedral prisms, 6 pentagonal-octagonal duoprisms, 8 pentagonal-hexagonal duoprisms, and 8 square-pentagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-pentagonal duoprism, 1 pentagonal-hexagonal duoprism, and 1 pentagonal-octagonal duoprism.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

Klitzing, Richard. "n-girco-dip".