# Decagonal-icosahedral duoprism

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Decagonal-icosahedral duoprism | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Dike |

Coxeter diagram | x10o o5o3x () |

Elements | |

Tera | 20 triangular-decagonal duoprisms, 10 icosahedral prisms |

Cells | 200 triangular prisms, 30 decagonal prisms, 10 icosahedra |

Faces | 200 triangles, 300 squares, 12 decagons |

Edges | 120+300 |

Vertices | 120 |

Vertex figure | Pentagonal scalene, edge lengths 1 (base pentagon), √(5+√5)/2 (top), √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Ipe–ike–ipe: 144° |

Tradedip–dip–tradedip: | |

Tradedip–trip–ipe: 90° | |

Central density | 1 |

Number of external pieces | 30 |

Level of complexity | 10 |

Related polytopes | |

Army | Dike |

Regiment | Dike |

Dual | Decagonal-dodecahedral duotegum |

Conjugate | Decagrammic-great icosahedral duoprism |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×I_{2}(10), order 2400 |

Convex | Yes |

Nature | Tame |

The **decagonal-icosahedral duoprism** or **dike** is a convex uniform duoprism that consists of 10 icosahedral prisms and 20 triangular-decagonal duoprisms. Each vertex joins 2 icosahedral prisms and 5 triangular-decagonal duoprisms.

## Vertex coordinates[edit | edit source]

The vertices of a triangular-icosahedral duoprism of edge length 1 are given by all even permutations of the last three coordinates of:

## Representations[edit | edit source]

A decagonal-icosahedral duoprism has the following Coxeter diagrams:

- x10o o5o3x () (full symmetry)
- x5x o5o3x () (decagons as dipentagons)

## External links[edit | edit source]

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