# Cube atop small rhombicuboctahedron

Cube atop small rhombicuboctahedron | |
---|---|

Rank | 4 |

Type | Segmentotope |

Space | Spherical |

Notation | |

Bowers style acronym | Cubasirco |

Coxeter diagram | xx4oo3ox&#x |

Elements | |

Cells | 8 tetrahedra, 12 triangular prisms, 1+6 cubes, 1 small rhombicuboctahedron |

Faces | 8+24 triangles, 6+6+12+24 squares |

Edges | 12+24+24+24 |

Vertices | 8+24 |

Vertex figures | 8 triangular antipodiums, edge lengths 1 (base 1) and √2 (base 2 and sides) |

24 isosceles trapezoidal pyramids, base edge lengths 1, √2, √2, √2, side edge lengths 1, 1, √2. √2 | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–trip: 150° |

Cube–4–trip: | |

Cube–4–cube: 135° | |

Sirco–3–tet: 60° | |

Sirco–4–trip: | |

Sirco–4–cube: 45° | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Cubasirco |

Regiment | Cubasirco |

Dual | Octahedral-deltoidal icositetrahedral tegmoid |

Conjugate | Cube atop quasirhombicuboctahedron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I, order 48 |

Convex | Yes |

Nature | Tame |

The **cube atop small rhombicuboctahedron**, or **cubasirco**, is a CRF segmentochoron (designated K-4.71 on Richard Klitzing's list). As the name suggests, it consists of a cube and a small rhombicuboctahedron as bases, connected by 8 tetrahedra, 12 triangular prisms, and 6 further cubes.

It is also sometimes referred to as a **cubic cupola**, as one generalization of the definition of a cupola is to have a polytope atop an expanded version.

A small disprismatotesseractihexadecachoron can be formed by attaching cube atop small rhombicuboctahedron segmentochora to the bases of the small rhombicuboctahedral prism.

## Segmentochoron display[edit | edit source]

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a cube atop small rhombicuboctahedron of edge length 1 are given by:

along with all permutations of the first three coordinates of:

## External links[edit | edit source]

- Klitzing, Richard. "cubasirco".

- Wikipedia Contributors. "Cubic cupola".