# Square-decagonal duoprism

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Square-decagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Squadedip |

Coxeter diagram | x4o x10o () |

Elements | |

Cells | 10 cubes, 4 decagonal prisms |

Faces | 10+40 squares, 4 decagons |

Edges | 40+40 |

Vertices | 40 |

Vertex figure | Digonal disphenoid, edge lengths √(5+√5)/2 (base 1) and √2 (base 2 and sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–cube: 144° |

Dip–10–dip: 90° | |

Cube–4–dip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 14 |

Level of complexity | 6 |

Related polytopes | |

Army | Squadedip |

Regiment | Squadedip |

Dual | Square-decagonal duotegum |

Conjugate | Square-decagrammic duoprism |

Abstract & topological properties | |

Flag count | 960 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×I_{2}(10), order 160 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **square-decagonal duoprism** or **squadedip**, also known as the **4-10 duoprism**, is a uniform duoprism that consists of 4 decagonal prisms and 10 cubes, with two of each joining at each vertex.

It is a prism based on the decagonal prism. As such it is also a CRF segmentochoron, designated K-4.97 on Richard Klitzing's list.

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

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

Coordinates for the vertices of a square-decagonal duoprism with edge length 1 are given by:

- ,
- ,
- .

## Representations[edit | edit source]

A square-decagonal duoprism has the following Coxeter diagrams:

- x4o x10o () (full symmetry)
- x4o x5x () (B
_{2}×H_{2}symmetry, decagon as dipentagon) - x x x10o () (I
_{2}(10)×K_{2}symmetry, square as rectangle) - x x x5x () (H
_{2}×K_{2}symmetry, both above) - xx xx10oo (I
_{2}(10)×A_{1}symmetry, decagon prismatic prism) - xx xx5xx&#x (H
_{2}×A_{1}axial, as above) - oqo xxx10ooo&#xt
- oqo xxx5xxx&#xt (H
_{2}×A_{1}axial, decagon-first)

## External links[edit | edit source]

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

- Klitzing, Richard. "squadedip".