# Snub hexecontatetrasnub-snub disoctachoron

The **snub hexecontatetrasnub-snub disoctachoron**, or **siggissido**, is a nonconvex uniform polychoron that consists of 8 icosahedra, 8 great icosahedra, 64+96 regular octahedra, and 192 tetrahedra. 1 icosahedron, 1 great icosahedron, 4+6 octahedra, and 8 tetrahedra join at each vertex.

Snub hexecontatetrasnub-snub disoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Siggissido |

Elements | |

Cells | 192 tetrahedra, 64+96 octahedra, 8 icosahedra, 8 great icosahedra |

Faces | 64+64+96+96+96+192+192+192+192 triangles |

Edges | 48+96+96+192+192+192 |

Vertices | 96 |

Vertex figure | Blend of pentagrammic cuploid and retropentagonal cuploid, edge length 1 |

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | Undefined |

Related polytopes | |

Army | Sadi |

Regiment | Disdi |

Conjugate | Snub hexecontatetrasnub-snub disoctachoron |

Convex core | Tesseract |

Abstract & topological properties | |

Euler characteristic | –224 |

Orientable | No |

Properties | |

Symmetry | B_{4}/2, order 192 |

Convex | No |

Nature | Tame |

This polychoron has pyritotesseractic symmetry, with the icosahedra and great icosahedra acting as snub tetrahedra. It can be thought as a kind of sub-symmetrical faceting of the small stellated hecatonicosachoron. With all of its cells geometrically regular, it can be considered a semiregular polychoron.

It was discovered on January 28, 2021, by Polytope Discord user _Geometer. Following the discovery of six uniforms the previous year its discovery led to the find of several hundred additional uniforms in the same regiment.

## Gallery edit

## Vertex coordinates edit

The vertices of a snub hexecontatetrasnub-snub disoctachoron of edge length 1, centered at the origin, are given by all even permutations of:

## External links edit

- Bowers, Jonathan. "Category 30: Idtessids" (#1856).