# Great prismatodemipenteract

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Great prismatodemipenteract | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Giphin |

Coxeter diagram | x3x3x3x *b3o () |

Elements | |

Tera | 40 truncated tetrahedral prisms, 16 great rhombated pentachora, 10 tesseractihexadecachora, 16 great prismatodecachora |

Cells | 160 triangular prisms, 80+160 hexagonal prisms, 80+80 truncated tetrahedra, 80+80 truncated octahedra |

Faces | 320 triangles, 240+240+480 squares, 160+320+320 hexagons |

Edges | 480+480+480+960 |

Vertices | 960 |

Vertex figure | Sphenoidal pyramid, edge lengths 1 (1), √2(4), and √3 (5) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Grip–trip–tuttip: |

Tah–tut–tuttip: 135° | |

Gippid–hip–tuttip: | |

Grip–toe–gippid: | |

Tah–toe–grip: | |

Tah–tut–grip: | |

Gippid–hip–gippid: | |

Central density | 1 |

Number of external pieces | 82 |

Level of complexity | 60 |

Related polytopes | |

Army | Giphin |

Regiment | Giphin |

Dual | Sphenoidal-pyramidal enneacosihexecontateron |

Conjugate | None |

Abstract & topological properties | |

Flag count | 115200 |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | D_{5}, order 1920 |

Convex | Yes |

Nature | Tame |

The **great prismatodemipenteract**, or **giphin**, also called the **steriruncicantic 5-cube**, is a convex uniform polyteron. It consists of 40 truncated tetrahedral prisms, 16 great rhombated pentachora, 10 tesseractihexadecachora, and 16 great prismatodecachora. 2 great prismatodecachora, 1 great rhombated pentachoron, 1 tesseractihexadecachoron, and 1 trunctaed tetrahedral prism join at each vertex. It can be formed from an alternated faceting of the celligreatorhombated triacontaditeron.

## Vertex coordinates[edit | edit source]

The vertices of a great prismatodemipenteract of edge length 1 are given by all permutations and even sign changes of:

- .

## Representations[edit | edit source]

A great prismatodemipenteract has the following Coxeter diagrams:

- x3x3x3x *b3o () (full symmetry)
- s4o3x3x3x () (as alternated faceting)

## Gallery[edit | edit source]

## Related polytopes[edit | edit source]

Name | OBSA | CD diagram | Picture |
---|---|---|---|

Demipenteract | hin | ||

Penteractitriacontaditeron | nit | ||

Rectified triacontaditeron | rat | ||

Triacontaditeron | tac | ||

Truncated demipenteract | thin | ||

Bitruncated triacontaditeron | bittit | ||

Truncated triacontaditeron | tot | ||

Rectified penteract | rin | ||

Small rhombidemipenteract | sirhin | ||

Small rhombated triacontaditeron | sart | ||

Bitruncated penteract | bittin | ||

Great rhombidemipenteract | girhin | ||

Great rhombated triacontaditeron | gart | ||

Small birhombated penteract | sibrant | ||

Great birhombated penteract | gibrant | ||

Small prismatodemipenteract | siphin | ||

Prismatotruncatodemipenteract | pithin | ||

Prismatorhombidemipenteract | pirhin | ||

Great prismatodemipenteract | giphin | ||

Small prismated triacontaditeron | spat | ||

Prismatorhombated triacontaditeron | pirt | ||

Prismatotruncated triacontaditeron | pattit | ||

Great prismated triacontaditeron | gippit |

## External links[edit | edit source]

- Bowers, Jonathan. "Category 10: Greater Truncates" (#741).

- Klitzing, Richard. "giphin".

- Wikipedia Contributors. "Steriruncicantic 5-cube".