# Demipenteract

Demipenteract | |
---|---|

Rank | 5 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Hin |

Coxeter diagram | x3o3o *b3o3o () |

Elements | |

Tera | 16 pentachora, 10 hexadecachora |

Cells | 40+80 tetrahedra |

Faces | 160 triangles |

Edges | 80 |

Vertices | 16 |

Vertex figure | Rectified pentachoron, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Diteral angles | Hex–tet–pen: |

Hex–tet–hex: 90° | |

Height | |

Central density | 1 |

Number of pieces | 26 |

Level of complexity | 3 |

Related polytopes | |

Army | Hin |

Regiment | Hin |

Dual | Semistellated triacontaditeron |

Conjugate | None |

Abstract properties | |

Flag count | 5760 |

Euler characteristic | 2 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | D_{5}, order 1920 |

Convex | Yes |

Nature | Tame |

The **demipenteract**, or **hin**, also called the **hemipenteract** or **5-demicube**, is a convex uniform polyteron. It has 10 hexadecachora and 16 pentachora as facets, with 5 of each at a vertex forming a rectified pentachoron as the vertex figure. It is the 5-dimensional demihypercube and is formed by alternating the penteract.

This is the lowest-dimesional demihypercube that is not identical to another regular polytope of the same dimension.

It is also a convex segmentoteron, as a hexadecachoron atop rotated hexadecachoron, or hexadecachoric alterprism. It is also the digonal-tetrahedral duoantiprism.

## Vertex coordinates[edit | edit source]

The vertices of a demipenteract of edge length 1, centered at the origin, are given by all even sign changes of:

## Representations[edit | edit source]

A demipenteract has the following Coxeter diagrams:

- x3o3o *b3o3o (full symmetry)
- s4o3o3o3o (as alternated penteract)
- xo3oo3ox *b3oo&#x (D4 axial, demitesseractic alterprism)
- ooo3oxo3ooo3oox&#xt (A4 axial, vertex-first)
- xox3ooo3oxo oxo&#xt (A3×A1 axial, tetrahedron-first)
- xo3oo3ox xo ox&#zx (A3×A1×A1 symmetry)
- xoxo oxox oxoo3ooxo&#xt (A2×A1×A1 axial, edge-first)

## Related polytopes[edit | edit source]

The demipenteract is the colonel of a 6-member regiment. Its other members include the dishexadecateron, hexadecapenteract, retrodishexadecateron, retropenteractihexadecateron, and the noble hexadecateron.

The hollow stellated icositetrachoric antiprism can be constructed as a blend of 6 demipenteracts.

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 1: Primary Polytera" (#7).

- Klitzing, Richard. "hin".

- Wikipedia Contributors. "5-demicube".