# Great cellidodecateron

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Great cellidodecateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Gocad |

Coxeter diagram | x3x3x3x3x () |

Elements | |

Tera | 20 hexagonal duoprisms, 30 truncated octahedral prisms, 12 great prismatodecachora |

Cells | 90 cubes, 120+120+120 hexagonal prisms, 30+60 truncated octahedra |

Faces | 180+180+360+360 squares, 240+240 hexagons |

Edges | 360+720+720 |

Vertices | 720 |

Vertex figure | Phyllic disphenoidal pyramid, edge lengths √2 (6) and √3 (4) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Tope–hip–hiddip: 135° |

Gippid–toe–tope: | |

Tope–cube–tope: 120° | |

Gippid–hip–hiddip: | |

Gippid–hip–tope: | |

Gippid–toe–gippid: | |

Central density | 1 |

Number of external pieces | 62 |

Level of complexity | 60 |

Related polytopes | |

Army | Gocad |

Regiment | Gocad |

Dual | Disphenoidal pyramidal heptacosiicosateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}×2, order 1440 |

Convex | Yes |

Nature | Tame |

The **great cellidodecateron**, or **gocad**, also called the **great cellated hexateron** or **omnitruncated 5-simplex**, is a convex uniform polyteron. It consists of 20 hexagonal duoprisms, 30 truncated octahedral prisms, and 12 great prismatodecachora. 2 great prismatodecachora, 2 truncated octahedral prisms, and 1 hexagonal duoprism join at each vertex. As the name suggests, it is the omnitruncate of the A_{5} family.

This polyteron can be alternated into a snub dodecateron, but that cannot be made uniform.

It is the 6th-order permutohedron, and therefore fills 5D space.

## Vertex coordinates[edit | edit source]

The vertices of a great cellidodecateron 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" (#742).

- Klitzing, Richard. "gocad".

- Wikipedia Contributors. "Omnitruncated 5-simplex".