# Octahedron atop cube

Jump to navigation
Jump to search

Octahedron atop cube | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Octacube |

Coxeter diagram | xo4oo3ox&#x |

Elements | |

Cells | 8+12 tetrahedra, 6 square pyramids, 1 octahedron, 1 cube |

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

Edges | 12+12+24 |

Vertices | 6+8 |

Vertex figures | 6 square antiprisms, edge length 1 |

8 triangular antipodiums, edge lengths √2 (large base) and 1 (small base and sides) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–tet: |

Tet–3–oct: | |

Tet–3–squippy: | |

Cube–4–squippy: | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Octacube |

Regiment | Octacube |

Dual | Cubic-octahedral tegmoid |

Conjugate | Octahedron atop cube |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×I, order 48 |

Convex | Yes |

Nature | Tame |

The **octahedron atop cube**, or **octacube**, is a CRF segmentochoron (designated K-4.15 on Richard Klitzing's list). As the name suggests, it consists of a cube and an octahedron as bases, connected by 6 square pyramids and 8+12 tetrahedra.

It is also commonly referred to as a cubic or octahedral antiprism, as the two bases are a pair of dual polyhedra.

## Vertex coordinates[edit | edit source]

The vertices of an octahedron atop cube segmentochoron of edge length 1 are given by:

- and all permutations of its first 3 coordinates,

## External links[edit | edit source]

- Klitzing, Richard. "octacube".
- Quickfur. "The Cube Antiprism".