# Celliprismatotruncatododecateron

Celliprismatotruncatododecateron | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Captid |

Coxeter diagram | x3x3o3x3x () |

Elements | |

Tera | 30 truncated tetrahedral prisms, 20 hexagonal duoprisms, 12 prismatorhombated pentachora |

Cells | 120 triangular prisms, 120+120 hexagonal prisms, 60 truncated tetrahedra, 30 cuboctahedra |

Faces | 240 triangles, 90+180+360 squares, 240 hexagons |

Edges | 360+720 |

Vertices | 360 |

Vertex figure | Rectangular scalene, base edge lengths 1 and √2, remaining edge lengths √2 (5) and √3 (4) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

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

Prip–tut–tuttip: | |

Prip–hip–hiddip: | |

Prip–trip–tuttip: | |

Prip–co–prip: | |

Central density | 1 |

Number of external pieces | 62 |

Level of complexity | 40 |

Related polytopes | |

Army | Captid |

Regiment | Captid |

Dual | Rhombipyramidal pyramidal triacosihexecontateron |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | A_{5}×2, order 1440 |

Convex | Yes |

Nature | Tame |

The **celliprismatotruncatododecateron**, or **captid**, also called the **celliprismatotruncated hexateron** or **steriruncitruncated 5-simplex**, is a convex uniform polyteron. It consists of 30 truncated tetrahedral prisms, 20 hexagonal duoprisms, and 12 prismatorhombated pentachora. 2 prismatorhombated pentachora, 2 truncated tetrahedral prisms, and 2 hexagonal duoprisms join at each vertex. As the name suggests, it is the steriruncitruncation of the hexateron.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A celliprismatotruncatododecateron has the following Coxeter diagrams:

- x3x3o3x3x (full symmetry)
- xxxux3xxxoo3ooxxx3xuxxx&#xt (A
_{4}axial, prismatorhombated pentachoron-first)

## Gallery[edit | edit source]

## Related polytopes[edit | edit source]

The celliprismatotruncatododecateron is the colonel of a three-member regiment that also includes the retrocelliprismatotruncatododecateron and lepidocelliprismatotruncatododecateron.

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 13: Prismatorhombates and Kin" (#844).

- Klitzing, Richard. "captid".

- Wikipedia Contributors. "Steriruncitruncated 5-simplex".