# Great retroinverted dodecahedronary prismatohecatonicosachoron

The **great retroinverted dodecahedronary prismatohecatonicosachoron**, or **gridaphi**, is a nonconvex uniform polychoron that consists of 120 icosahedra and 1200 triangular prisms. Twelve icosahedra and sixty triangular prisms join at each vertex.

Great retroinverted dodecahedronary prismatohecatonicosachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Gridaphi |

Elements | |

Cells | 120 ike, 1200 trip |

Faces | 2400 triangles, 1800 squares |

Edges | 1200 |

Vertices | 120 |

Edge figure | (ike 3 trip 4 trip 4 trip 3)×3 |

Measures (edge length 1) | |

Circumradius | 1 |

Number of external pieces | 237600 |

Level of complexity | 524 |

Related polytopes | |

Army | Ex |

Regiment | Sishi |

Conjugate | Sridaphi |

Abstract & topological properties | |

Euler characteristic | 1800 |

Orientable | Yes |

Properties | |

Symmetry | H_{4}, order 14400 |

Convex | No |

Nature | Feral |

It also has great icosahedra and tetrahedra as pseudofacets.

## Vertex coordinates edit

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

## External links edit

- Bowers, Jonathan. "Category 17: Sishi Regiment" (#775).

- Klitzing, Richard. "gridaphi".

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