# Small ditetrahedronary hexacosihecatonicosachoron

Small ditetrahedronary hexacosihecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sidtaxhi |

Coxeter diagram | o3o3x5/2o3*b () |

Elements | |

Cells | 600 tetrahedra, 120 small ditrigonary icosidodecahedra |

Faces | 2400 triangles, 720 pentagrams |

Edges | 3600 |

Vertices | 600 |

Vertex figure | Semi-uniform Truncated tetrahedron, edge lengths 1 (triangle edges) and (√5–1)/2 (other edges) |

Edge figure | (tet 3 sidtid 5/2 sidtid 3) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Sidtid–3–tet: |

Sidtid–5/2–sidtid: 144° | |

Central density | 2 |

Number of external pieces | 2520 |

Level of complexity | 9 |

Related polytopes | |

Army | Hi, edge length |

Regiment | Sidtaxhi |

Conjugate | Grand ditetrahedronary hexacosihecatonicosachoron |

Abstract & topological properties | |

Flag count | 43200 |

Euler characteristic | —600 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Tame |

The **small ditetrahedronary hexacosihecatonicosachoron**, or **sidtaxhi**, is a nonconvex uniform polychoron that consists of 600 regular tetrahedra and 120 small ditrigonary icosidodecahedra. 4 small ditrigonary icosidodecahedra and 4 tetrahedra join at each vertex, with a variant of the truncated tetrahedron as the vertex figure.

The small ditetrahedronary hexacosihecatonicosachoron contains the vertices of a small rhombicosidodecahedral prism and decagonal duoprism.

It can be formed as a holosnub hecatonicosachoron.

## Vertex coordinates[edit | edit source]

The vertices of a small ditetrahedronary hexacosihecatonicosachoron of edge length 1, centered at the origin, are given by all permutations of:

together with all the even permutations of:

## Related polychora[edit | edit source]

The small ditetrahedronary hexacosihecatonicosachoron is the colonel of a regiment with 37 members, plus 5 fissaries and three compounds (two are subsymmetric), as well as 11 scaliform members plus 54 scaliform fissaries and 2 scaliform compounds.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 18: Ditetrahedrals" (#778).

- Bowers, Jonathan. "How to Make Sidtaxhi".

- Klitzing, Richard. "sidtaxhi".