# Excavated truncated rhombicuboctahedron

Excavated truncated rhombicuboctahedron | |
---|---|

Rank | 3 |

Type | Quasi-convex Stewart toroid |

Elements | |

Faces | 8 triangles, 6+24+24+24+48 squares, 8 hexagons, 6 octagons |

Edges | 24+24+24+24+24+24+24+48+48+48 |

Vertices | 24+24+48+48 |

Measures (edge length 1) | |

Volume | |

Surface area | |

Dihedral angles | 4-4 (op lacing, narrow): |

4-4 (op lacing, wide): | |

4-6 (tricu to trip): | |

4-8 (squacu to trip): | |

4-4 (in squacu): 135° | |

3-4 (in tricu): | |

4-4 (trip lacings): 60° | |

4–6 (in tricu): | |

4-8 (in squacu): 45° | |

Related polytopes | |

Convex hull | Truncated rhombicuboctahedron |

Abstract & topological properties | |

Flag count | 1248 |

Euler characteristic | –20 |

Orientable | Yes |

Genus | 11 |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 26 |

Convex | No |

Nature | Tame |

History | |

Discovered by | Alex Doskey |

First discovered | 2004 |

The **excavated truncated rhombicuboctahedron** is a quasi-convex Stewart toroid. It can be obtained by excavating 12 unit-edge-length irregular octagonal prisms from a truncated rhombicuboctahedron, then excavating the central polyhedron as well (blending it with the remaining irregular-octagon faces of the prisms and opening up that space). Since the irregular faces are all blended away, the toroid is regular-faced. Its convex hull is an equilateral truncated rhombicuboctahedron, with 6 regular octagons, 12 rectangular-symmetric octagons, 8 hexagons, and 24 squares.

The central polyhedron is a truncation of the rhombic dodecahedron that cuts away both types of vertices, with 6 squares, 8 triangles, and 12 rectangular-symmetric octagons.

The excavated truncated rhombicuboctahedron can also be obtained by outer-blending six square cupolae, eight triangular cupolae, and twenty-four triangular prisms together.

## Vertex coordinates[edit | edit source]

This polytope is missing vertex coordinates. (April 2024) |

## Related polyhedra[edit | edit source]

If the cupolae are "contracted" into pyramids (by removing the side squares and pulling the side triangle faces together, like the opposite of a partial expansion), an excavated expanded cuboctahedron will be formed.

If the triangular prisms are removed (and the cupolae brought together), a truncated cuboctahedron excavated with cubes and a central small rhombicuboctahedron will be formed.

## External links[edit | edit source]

- Wikipedia contributors. "Excavated truncated rhombicuboctahedron".
- Doskey, Alex. "Prism Expansions".