# Snub cellibiprismatoteron

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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. 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. "Polyhedron Category 6: Snubs" (#64).

- Klitzing, Richard. "Snic".
- Quickfur. "The Snub Cube".

- Wikipedia contributors. "Snub cube".
- McCooey, David. "Snub Cube"

- Hi.gher.Space Wiki Contributors. "Snub staurohedron".