# Decagonal duoprism

The **decagonal duoprism** or **dedip**, also known as the **decagonal-decagonal duoprism**, the **10 duoprism** or the **10-10 duoprism**, is a noble uniform duoprism that consists of 20 decagonal prisms, with four at each vertex. It is also the 20-9 gyrochoron. It is the first in an infinite family of isogonal decagonal dihedral swirlchora and also the first in an infinite family of isochoric decagonal hosohedral swirlchora.

Decagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Dedip |

Coxeter diagram | x10o x10o () |

Elements | |

Cells | 20 decagonal prisms |

Faces | 100 squares, 20 decagons |

Edges | 200 |

Vertices | 100 |

Vertex figure | Tetragonal disphenoid, edge lengths √(5+√5)/2 (bases) and √2 (sides) |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Hypervolume | |

Dichoral angles | Dip–10–dip: 144º |

Dip–4–dip: 90° | |

Central density | 1 |

Number of external pieces | 20 |

Level of complexity | 3 |

Related polytopes | |

Army | Dedip |

Regiment | Dedip |

Dual | Decagonal duotegum |

Conjugate | Decagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | I_{2}(10)≀S_{2}, order 800 |

Convex | Yes |

Nature | Tame |

This polychoron can be alternated into a pentagonal duoantiprism, although it cannot be made uniform.

A unit decagonal duoprism can be edge-inscribed into the small ditetrahedronary hexacosihecatonicosachoron.

## GalleryEdit

Wireframe, cell, net

## Vertex coordinatesEdit

Coordinates for the vertices of a decagonal duoprism of edge length 1, centered at the origin, are given by:

## RepresentationsEdit

A decagonal duoprism has the following Coxeter diagrams:

- x10o x10o (full symmetry)
- x5x x10o (one decagon as dipentagon)
- x5x x5x (both decagons have pentagonal symmetry)

## External linksEdit

- Bowers, Jonathan. "Category A: Duoprisms".

- Bowers, Jonathan. "Four Dimensional Dice Up To Twenty Sides".

- Klitzing, Richard. "dadip".

- Wikipedia Contributors. "10-10 duoprism".