# Demihepteract

(Redirected from 7-demicube)

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Demihepteract | |
---|---|

Rank | 7 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Hesa |

Info | |

Coxeter diagram | |

Symmetry | D7, order 322560 |

Army | Hesa |

Regiment | Hesa |

Elements | |

Vertex figure | Rectified heptapeton, edge length 1 |

Exa | 64 heptapeta, 14 demihexeracts |

Peta | 448 hexatera, 84 demipenteracts |

Tera | 1344 pentachora, 280 hexadecachora |

Cells | 560+2240 tetrahedra |

Faces | 2240 triangles |

Edges | 672 |

Vertices | 64 |

Measures (edge length 1) | |

Circumradius | √14/4 ≈ 0.93541 |

Hypervolume | 311√2/5040 ≈ 0.087266 |

Diexal angles | Hax–hix–hop: acos(–√7/7) ≈ 112.20765° |

Hax–hin–hax: 90° | |

Height | √2/2 ≈ 0.70711 |

Central density | 1 |

Euler characteristic | 2 |

Related polytopes | |

Dual | Semistellated hecatonicosoctaexon |

Conjugate | Demihepteract |

Properties | |

Convex | Yes |

Orientable | Yes |

Nature | Tame |

The **demihepteract**, or **hesa**, also called the **hemihepteract** or **7-demicube**, is a convex uniform polyexon. It has 14 demihexeracts and 64 heptapeta as facets, with 7 of each at a vertex forming a rectified heptapeton as the vertex figure. It is the 7-dimensional demihypercube and is formed by alternating the hepteract. It is also a segmentopeton, as a demihexeractic antiprism.

The demihepteract contains the vertices of a tetrahedral-hexadecachoric duoprism.

## Vertex coordinates[edit | edit source]

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

- (√2/4, √2/4, √2/4, √2/4, √2/4, √2/4, √2/4).

## Representations[edit | edit source]

A demihepteract has the folowing Coxeter diagrams:

- x3o3o *b3o3o3o3o (full symmetry)
- s4o3o3o3o3o3o (as alternated hepteract)
- xo3oo3ox *b3oo3oo3oo&#x (D6 axial, demihexeract antiprism)
- oooo3oxoo3oooo3ooxo3oooo3ooox&#xt (A6 axial, vertex-first)
- oxoo3ooxo xoxo3oooo3oxox *d3oooo&#xt (D4×A2 symmetry, hexadecachoron-first)
- xo3oo3ox *b3oo xo3oo3ox&#zx (D4×A3 symmetry, hull of two tetrahedral-hexadecachoric duoprisms)

## External links[edit | edit source]

- Klitzing, Richard. "Hesa".

- Wikipedia Contributors. "7-demicube".