# Truncated small prismatotetracontoctachoron

Truncated small prismatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Tispic |

Elements | |

Cells | 144 square antiprisms, 192 truncated triangular prisms, 48 truncated octahedra |

Faces | 1152 isosceles triangles, 288 squares, 384 ditrigons, 288 ditetragons |

Edges | 576+1152+1152 |

Vertices | 1152 |

Vertex figure | Isosceles trapezoidal pyramid |

Measures (variant with hexagons of edge length 1) | |

Edge lengths | Edges of hexagons (576+1152): 1 |

Lacing edges (1152): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Tispic |

Regiment | Tispic |

Dual | Octakis square-antitegmatic hecatontetracontatetrachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **truncated small prismatotetracontoctachoron** or **tispic** is a convex isogonal polychoron that consists of 48 truncated octahedra, 192 truncated triangular prisms, and 144 square antiprisms. 1 square antiprism, 1 truncated octahedron, and 3 truncated triangular prisms join at each vertex. It can be formed by truncating the small prismatotetracontoctachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the prismatorhombated icositetrachoron, where if the prismatorhombated icositetrachora are of the form a3b4o3c, then c = a+2b. It is one of five polychora (including two transitional cases) formed from two prismatorhombated icositetrachora, and is the transitional point between the medial biprismatorhombatotetracontoctachoron and great biprismatorhombatotetracontoctachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.41421. This variant uses regular hexagons as faces.

## Vertex coordinates[edit | edit source]

The vertices of a truncated small prismatotetracontoctachoron of edge length 1, centered at the origin, are given by:

## External links[edit | edit source]

- Klitzing, Richard. "tispic".