# Square-pentagonal duoprism

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Square-pentagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Squipdip |

Coxeter diagram | x4o x5o () |

Elements | |

Cells | 5 cubes, 4 pentagonal prisms |

Faces | 5+20 squares, 4 pentagons |

Edges | 20+20 |

Vertices | 20 |

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

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–cube: 108° |

Pip–5–pip: 90° | |

Cube–4–pip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 9 |

Level of complexity | 6 |

Related polytopes | |

Army | Squipdip |

Regiment | Squipdip |

Dual | Square-pentagonal duotegum |

Conjugate | Square-pentagrammic duoprism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×H_{2}, order 80 |

Convex | Yes |

Nature | Tame |

The **square-pentagonal duoprism** or **squipdip**, also known as the **4-5 duoprism**, is a uniform duoprism that consists of 4 pentagonal prisms and 5 cubes, with two of each joining at each vertex.

It is also a CRF segmentochoron, being a pentagonal prism atop pentagonal prism. It is designated K-4.42 on Richard Klitzing's list. It can thus be thought of as a prism based on the pentagonal prism.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A suare-pentagonal duoprism has the following Coxeter diagrams:

- x4o x5o (full symmetry)
- x x x5o (H2×A1×A1 symmetry, square as rectangle)
- xx xx5oo#x (H2×A1 axial, pentagonal prism prism)
- ofx xxx4ooo&#xt (BC2×A1 axial, square-first)
- ofx xxx xxx&#xt (A1×A1×A1, as above with rectangle symmetry)
- oqo xxx5ooo&#xt (H2×A1 axial, pentagon-first)

## External links[edit | edit source]

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

- Klitzing, Richard. "squipdip".