# Retroinverted disicositetrachoron

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Retroinverted disicositetrachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Ridi |

Elements | |

Cells | 24 truncated cubes, 24 small cubicuboctahedra |

Faces | 192 triangles, 72 squares, 144 octagons |

Edges | 288+288 |

Vertices | 144 |

Vertex figure | Blend of two crossed wedges, edge lengths 1 (blended wedge bases), √2 (wedge tops), and √2+√2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Dichoral angles | Soccco–4–socco: 90° |

Socco–8–tic: 90° | |

Socco–3–tic: 60° | |

Related polytopes | |

Army | Spic |

Regiment | Spic |

Conjugate | Inverted disicositetrachoron |

Abstract & topological properties | |

Flag count | 8064 |

Euler characteristic | –72 |

Orientable | No |

Properties | |

Symmetry | F_{4}, order 1152 |

Convex | No |

Nature | Tame |

The **retroinverted disicositetrachoron**, or **ridi**, is a nonconvex uniform polychoron that consists of 24 truncated cubes and 24 small cubicuboctahedra. Four truncated cubes and four small cubicuboctahedra join at each vertex.

It can be constructed as the blend of 3 retrosphenoverted tesseractitesseractihexadecachora, with the octahedral cells blending out.

## Vertex coordinates[edit | edit source]

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

## External links[edit | edit source]

- Bowers, Jonathan. "Category 13: Spic and Giddic Regiments" (#523).

- Klitzing, Richard. "ridi".

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