# Small retrospinoprismatodisicositetrachoron

The **small retrospinoprismatodisicositetrachoron**, or **sarnipadi**, is a nonconvex uniform polychoron that consists of 24 truncated cubes, 24 small rhombihexahedra, and 96 triangular prisms. Four truncated cubes, four small rhombihexahedra, and four triangular prisms join at each vertex.

Small retrospinoprismatodisicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Sarnipadi |

Elements | |

Cells | 96 triangular prisms, 24 truncated cubes, 24 small rhombihexahedra |

Faces | 192 triangles, 288 squares, 144 octagons |

Edges | 576 |

Vertices | 144 |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Tic–3–trip: 90° |

Sroh–8–tic: 45° | |

Sroh–4–trip: | |

Number of external pieces | 5832 |

Level of complexity | 187 |

Related polytopes | |

Army | Spic |

Regiment | Spic |

Conjugate | Great retrospinoprismatodisicositetrachoron |

Abstract & topological properties | |

Flag count | 11520 |

Euler characteristic | 48 |

Orientable | No |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Feral |

It can be constructed as a blend of three small pseudorhombic prismatotesseracts. In the process the octagonal prisms blend into small rhombihexahedra.

## Vertex coordinates edit

Its vertices are the same as those of its regiment colonel, the small prismatotetracontoctachoron.

## External links edit

- Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#526).

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