# Compound of ten triangular prisms

(Redirected from Chirorhombicosahedron)

Compound of ten triangular prisms | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Kri |

Elements | |

Components | 10 triangular prisms |

Faces | 20 triangles, 30 squares |

Edges | 30+60 |

Vertices | 60 |

Vertex figure | Isosceles triangle, edge lengths 1, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–3: 90° |

4–4: 60° | |

Central density | 10 |

Number of external pieces | 180 |

Level of complexity | 30 |

Related polytopes | |

Army | Semi-uniform Ti, edge lengths (pentagons), (between ditrigons) |

Regiment | Kri |

Dual | Compound of ten triangular tegums |

Conjugate | Compound of ten triangular prisms |

Convex core | Rhombic triacontahedron |

Abstract & topological properties | |

Flag count | 360 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}+, order 60 |

Convex | No |

Nature | Tame |

The **chirorhombicosahedron**, **kri**, or **compound of ten triangular prisms** is a uniform polyhedron compound. It consists of 30 squares and 20 triangles, with one triangle and two squares joining at a vertex.

Its quotient prismatic equivalent is the triangular prismatic decayottoorthowedge, which is twelve-dimensional.

## Vertex coordinates[edit | edit source]

The vertices of a chirorhombicosahedron of edge length 1 are given by all permutations of:

plus all even permutations of:

- ,
- .

## Related polyhedra[edit | edit source]

This compound is chiral. The compound of the two enantiomorphs is the disrhombicosahedron.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C7: Chiral and Doubled Prismatics" (#44).

- Klitzing, Richard. "kri".
- Wikipedia contributors. "Compound of ten triangular prisms".