# Great prismated hexateron

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Great prismated hexateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gippix |

Coxeter diagram | x3x3x3x3o () |

Elements | |

Tera | 20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 great rhombated pentachora, 6 great prismatodecachora |

Cells | 60+60 triangular prisms, 60+60 hexagonal prisms, 30 truncated tetrahedra, 15+30 truncated octahedra |

Faces | 120 triangles, 90+180+180 squares, 60+60+120 hexagons |

Edges | 180+180+180+360 |

Vertices | 360 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tuttip–trip–thiddip: 135° |

Grip–tut–tuttip: | |

Grip–trip–thiddip: | |

Gippid–hip–thiddip: | |

Gippid–hip–tuttip: | |

Gippid–toe–grip: | |

Gippid–toe–gippid: | |

Central density | 1 |

Number of external pieces | 47 |

Level of complexity | 60 |

Related polytopes | |

Army | Gippix |

Regiment | Gippix |

Dual | Sphenoidal-pyramidal triacosihexecontateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}, order 720 |

Convex | Yes |

Nature | Tame |

The **great prismated hexateron**, or **gippix**, also called the **runcicantitruncated 5-simplex**, is a convex uniform polyteron. It consists of 20 triangular-hexagonal duoprisms, 15 truncated tetrahedral prisms, 6 small rhombated pentachora, and 6 great prismatodecachora. 2 great prismatodecachora, 1 great rhombated pentachoron, 1 truncated tetrahedral prism, and 1 triangular-hexagonal duoprism join at each vertex. As the name suggests, it is the runcicantitruncation of the hexateron.

## Vertex coordinates[edit | edit source]

The vertices of a great prismated hexateron of edge length 1 can be given in 6 dimensions as all permutations of:

## Gallery[edit | edit source]

## Related polytopes[edit | edit source]

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

Hexateron | hix | ||

Rectified hexateron | rix | ||

Dodecateron | dot | ||

Rectified hexateron | rix | ||

Hexateron | hix | ||

Truncated hexateron | tix | ||

Bitruncated hexateron | bittix | ||

Bitruncated hexateron | bittix | ||

Truncated hexateron | tix | ||

Small rhombated hexateron | sarx | ||

Small birhombidodecateron | sibrid | ||

Small rhombated hexateron | sarx | ||

Great rhombated hexateron | garx | ||

Great birhombidodecateron | gibrid | ||

Great rhombated hexateron | garx | ||

Small prismated hexateron | spix | ||

Small prismated hexateron | spix | ||

Prismatotruncated hexateron | pattix | ||

Prismatorhombated hexateron | pirx | ||

Prismatorhombated hexateron | pirx | ||

Prismatotruncated hexateron | pattix | ||

Great prismated hexateron | gippix | ||

Great prismated hexateron | gippix | ||

Small cellidodecateron | scad | ||

Celliprismated hexateron | cappix | ||

Cellirhombidodecateron | card | ||

Celligreatorhombated hexateron | cograx | ||

Celliprismated hexateron | cappix | ||

Celliprismatotruncatododecateron | captid | ||

Celligreatorhombated hexateron | cograx | ||

Great cellidodecateron | gocad |

## External links[edit | edit source]

- Bowers, Jonathan. "Category 10: Greater Truncates" (#733).

- Klitzing, Richard. "gippix".

- Wikipedia Contributors. "Runcicantitruncated 5-simplex".