# Great prismatotetracontoctachoron

Great prismatotetracontoctachoron | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gippic |

Coxeter diagram | x3x4x3x () |

Elements | |

Cells | 192 hexagonal prisms, 48 great rhombicuboctahedra |

Faces | 288+576 squares, 384 hexagons, 144 octagons |

Edges | 1152+1152 |

Vertices | 1152 |

Vertex figure | Phyllic disphenoid, edge lengths √2 (3), √3 (2), and √2+√2 (1) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Hip–4–hip: |

Girco–6–hip: 150° | |

Girco–4–hip: | |

Girco–8–girco: 135° | |

Central density | 1 |

Number of pieces | 240 |

Level of complexity | 12 |

Related polytopes | |

Army | Gippic |

Regiment | Gippic |

Dual | Disphenoidal chiliahecatonpentaconta-dichoron |

Conjugate | Great quasiprismatotetracontocta-choron |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | F_{4}×2, order 2304 |

Convex | Yes |

Nature | Tame |

The **great prismatotetracontoctachoron**, or **gippic**, also commonly called the **omnitruncated 24-cell**, is a convex uniform polychoron that consists of 192 hexagonal prisms and 48 great rhombicuboctahedra. 2 hexagonal prisms and 2 great rhombicuboctahedra join at each vertex. It is the omnitruncate of the F_{4} family of uniform polychora.

This polychoron can be alternated into a snub tetracontoctachoron, although it cannot be made uniform.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a great prismatotetracontoctachoron of edge length 1 are given by all permutations of:

## Representations[edit | edit source]

A great prismatotetracontoctachoron has the following Coxeter diagrams:

- x3x4x3x (full symmetry)
- xux4wxx3xxx3xwX&#zx (BC
_{4}symmetry)

## Semi-uniform variant[edit | edit source]

The great prismatotetracontoctachoron has a semi-uniform variant of the form x3y4y3x that maintains its full symmetry. This variant uses 48 great rhombicuboctahedra of form y4y3x and 192 ditrigonal prisms of form x x3y as cells, with 2 edge lengths.

With edges of length a and b (so that it is represented by a3b4b3a), its circumradius is given by .

If it has only single icositetrachoric symmetry, the variant is called a great disprismatoicositetricositetrachoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 9: Omnitruncates" (#332).

- Klitzing, Richard. "gippic".

- Quickfur. "The Omnitruncated 24-cell".

- Wikipedia Contributors. "Omnitruncated 24-cell".