# Small disprismatopentapentachoron

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Small disprismatopentapentachoron | |
---|---|

Rank | 4 |

Type | Semi-uniform |

Notation | |

Coxeter diagram | x3o3o3y |

Elements | |

Cells | 5+5 tetrahedra, 10+10 triangular prisms |

Faces | 20+20 triangles, 30 rectangles |

Edges | 30+30 |

Vertices | 20 |

Vertex figure | Triangular antipodium |

Measures (edge lengths a, b) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–trip: |

Tet–3–trip: | |

Central density | 1 |

Related polytopes | |

Dual | Trigonal-trapezohedral icosachoron |

Conjugate | Small disprismatopentapentachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A4, order 120 |

Convex | Yes |

Nature | Tame |

The **small disprismatopentapentachoron** is a convex semi-uniform polychoron that is a variant of the small prismatodecachoron with only regular pentachoric and not doubled pentachoric symmetry. As such it can be represented by x3o3o3y, and has 10 tetrahedra (of two types, sizes x and y) and 20 triangular prisms (two types, forms x y3o and y x3o) as cells, with two edge lengths.