# Quasitruncated hexahedron

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Quasitruncated hexahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Quith |

Coxeter diagram | x4/3x3o () |

Elements | |

Faces | 8 triangles, 6 octagrams |

Edges | 12+24 |

Vertices | 24 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 8/3–8/3: 90° |

8/3–3: | |

Central density | 7 |

Number of external pieces | 54 |

Level of complexity | 11 |

Related polytopes | |

Army | Sirco, edge length |

Regiment | Quith |

Dual | Great triakis octahedron |

Conjugate | Truncated cube |

Convex core | Octahedron |

Abstract & topological properties | |

Flag count | 144 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{3}, order 120 |

Flag orbits | 3 |

Convex | No |

Nature | Tame |

The **quasitruncated hexahedron**, the **quasitruncated cube**, or **quith**, also called the **stellated truncated hexahedron**, is a uniform polyhedron. It consists of 8 triangles and 6 octagrams. Each vertex joins one triangle and two octagrams. As the name suggests, it can be obtained by quasitruncation of the cube.

## Vertex coordinates[edit | edit source]

A quasitruncated hexahedron of edge length 1 has vertex coordinates given by all permutations and sign changes of

- .

## Related polyhedra[edit | edit source]

The quasitruncated rhombihedron is a uniform polyhedron compound composed of 5 quasitruncated hexahedra.

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category 2: Truncates" (#17).

- Klitzing, Richard. "quith".
- Wikipedia contributors. "Stellated truncated hexahedron".
- McCooey, David. "Stellated Truncated Hexahedron"