# Great disprismatopentapentachoron

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Great disprismatopentapentachoron | |
---|---|

Rank | 4 |

Type | Semi-uniform |

Notation | |

Coxeter diagram | a3b3c3d |

Elements | |

Cells | 10+10 ditrigonal prisms, 5+5 great rhombitetratetrahedra |

Faces | 30+30+30 rectangles, 20+20+20 ditrigons |

Edges | 60+60+60+60 |

Vertices | 120 |

Vertex figure | Irregular tetrahedron |

Measures (edge lengths a, b, c, d) | |

Circumradius | |

Dichoral angles | Dittip–4–dittip: |

Gratet–6–dittip: | |

Gratet–4–dittip: | |

Gratet–6–gratet: | |

Central density | 1 |

Related polytopes | |

Dual | Tetrahedral hecatonicosachoron |

Conjugate | Great disprismatopentapentachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A4, order 120 |

Convex | Yes |

Nature | Tame |

The **great disprismatopentapentachoron** is a convex semi-uniform polychoron that is a variant of the great prismatodecachoron with only regular pentachoric and not doubled pentachoric symmetry. As such it can be represented by a3b3c3d, and has 10 great rhombitetratetrahedra (of two types, forms a3b3c and b3c3d) and 20 ditrigonal prisms (two types, forms a c3d and d a3b) as cells, with 4 edge lengths. It is the most complex isogonal polytope generally possible with A4 symmetry.

It can generally be alternated into a snub pentachoron, which is also not uniform.