# Decagonal-great rhombicuboctahedral duoprism

Decagonal-great rhombicuboctahedral duoprism | |
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Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Dagirco |

Coxeter diagram | x10o x4x3x () |

Elements | |

Tera | 12 square-decagonal duoprisms, 8 hexagonal-decagonal duoprisms, 6 octagonal-decagonal duoprisms |

Cells | 120 cubes, 80 hexagonal prisms, 60 octagonal prisms, 24+24+24 decagonal prisms, 10 great rhombicuboctahedra |

Faces | 120+240+240+240 squares, 80 hexagons, 60 octagons, 48 decagons |

Edges | 240+240+240+480 |

Vertices | 480 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Squadedip–dip–hadedip: |

Gircope–girco–gircope: 144° | |

Squadedip–dip–odedip: 135° | |

Hadedip–dip–odedip: | |

Squadedip–cube–gircope: 90° | |

Hadedip–hip–gircope: 90° | |

Odedip–op–gircope: 90° | |

Central density | 1 |

Number of external pieces | 36 |

Level of complexity | 60 |

Related polytopes | |

Army | Dagirco |

Regiment | Dagirco |

Dual | Decagonal-disdyakis dodecahedral duotegum |

Conjugates | Decagrammic-great rhombicuboctahedral duoprism, Decagonal-quasitruncated cuboctahedral duoprism, Decagrammic-quasitruncated cuboctahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I2(10), order 960 |

Convex | Yes |

Nature | Tame |

The **decagonal-great rhombicuboctahedral duoprism** or **dagirco** is a convex uniform duoprism that consists of 10 great rhombicuboctahedral prisms, 6 octagonal-decagonal duoprisms, 8 hexagonal-decagonal duoprisms, and 12 square-decagonal duoprisms. Each vertex joins 2 great rhombicuboctahedral prisms, 1 square-decagonal duoprism, 1 hexagonal-decagonal duoprism, and 1 octagonal-decagonal duoprism.

This polyteron can be alternated into a pentagonal-snub cubic duoantiprism, although it cannot be made uniform. The great rhombicuboctahedra can be edge-snubbed to create a pentagonal-pyritohedral prismantiprismoid, which is also nonuniform.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A decagonal-great rhombicuboctahedral duoprism has the following Coxeter diagrams:

- x10o x4x3x () (full symmetry)
- x5x x4x3x ()(decagons as dipentagons)