# Snub cellibiprismatoteron

Snub cellibiprismatoteron | |
---|---|

Rank | 5 |

Type | Uniform |

Notation | |

Bowers style acronym | Scab |

Elements | |

Tera | 160+480 triangular-square duoprisms, 80 snub cubic prisms |

Cells | 240+640 triangular prisms, 240+480+480 cubes, 80 snub cubes |

Faces | 640+1920 triangles, 480+960+960+1920 squares |

Edges | 960+1920+1920 |

Vertices | 960 |

Measures (edge length 1) | |

Circumradius | ≈ 1.51841 |

Related polytopes | |

Army | Semi-uniform Stericantellated 5-cube |

Regiment | Scab |

Conjugate | Self |

Abstract & topological properties | |

Flag count | 337920 |

Orientable | No |

Properties | |

Symmetry | B_{5}+, order 1920 |

Convex | No |

Nature | Tame |

The **snub cellibiprismatoteron** or **scab** is a nonconvex uniform 5-polytope. It consists of 160 triangular-square duoprisms forming 80 pairs, 480 more triangular-square duoprisms, and 80 snub cubic prisms, as well as 10 compounds of 6 tesseracts as pseudofacets. 2+6 triangular-square duoprisms and 4 snub cubic prisms meet at each vertex.

The snub cellibiprismatoteron is the first known non-multiprismatic uniform polytope to contain snub cubes as proper elements, in this case as ridges, with the same degrees of freedom (including scaling) and the same number of edge lengths as the snub cube. However, it can still be constructed by blending 20 square-snub cubic duoprisms on their tesseracts, hence the 6-tesseract pseudo-facets.

## Vertex coordinates[edit | edit source]

The vertices of a snub cellibiprismatoteron of edge length 1 are given by all permutations and sign changes of

- (
*c*,_{1}*c*,_{1}*c*,_{2}*c*,_{2}*c*),_{3}

where

- ,
- ,
- .

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Miscellaneous" (#1298).