# Compound of five small rhombicuboctahedra

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Compound of five small rhombicuboctahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Rasseri |

Elements | |

Components | 5 small rhombicuboctahedra |

Faces | 40 triangles as 20 hexagrams, 30+60 squares |

Edges | 120+120 |

Vertices | 120 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–3: |

4–4: 135° | |

Central density | 5 |

Number of external pieces | 1080 |

Level of complexity | 68 |

Related polytopes | |

Army | Semi-uniform Grid, edge lengths (dipentagon-ditrigon), (dipentagon-rectangle), (ditrigon-rectangle) |

Regiment | Rasseri |

Dual | Compound of five deltoidal icositetrahedra |

Conjugate | Compound of five quasirhombicuboctahedra |

Abstract & topological properties | |

Flag count | 960 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **rhombisnub rhombicosicosahedron**, **rasseri**, or **compound of five small rhombicuboctahedra ** is a uniform polyhedron compound. It consists of 40 triangles (which form coplanar pairs combining into 20 hexagrams) and 30+60 squares, with one triangle and three squares joining at each vertex. It can be seen as the cantellation of the rhombihedron.

Its quotient prismatic equivalent is the pyritosnub cubic pentachoroorthowedge, which is seven-dimensional.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a rhombisnub rhombicosicosahedron of edge length 1 can be given by all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C3: Fivers" (#15).

- Klitzing, Richard. "rasseri".
- Wikipedia contributors. "Compound of five rhombicuboctahedra".