# Retrograde pentagonal cuploid

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Retrograde pentagonal cuploid | |
---|---|

Rank | 3 |

Type | Segmentotope |

Space | Spherical |

Notation | |

Bowers style acronym | Rapescu |

Elements | |

Faces | 5 triangles, 5 squares, 1 pentagon |

Edges | 5+5+10 |

Vertices | 5+5 |

Vertex figures | 5 isosceles trapezoids, edge lengths 1, √2, (1+√5)/2, √2 |

5 butterflies, edge lengths 1, √2, 1, √2 | |

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 5–4: |

3–4: | |

Height | |

Related polytopes | |

Army | Pentagonal frustum |

Conjugate | Pentagrammic cuploid |

Abstract & topological properties | |

Euler characteristic | 1 |

Orientable | No |

Genus | 1 |

Properties | |

Symmetry | H_{2}×I, order 10 |

Convex | No |

Nature | Tame |

The **retrograde pentagonal cuploid**, also called the **retrograde pentagonal semicupola** or **rapescu**, is an orbiform polyhedron. It consists of 5 triangles, 5 squares, and 1 pentagon. It is a cuploid based on the pentagon seen as {5/4}, with a pseudo {10/4} base.

## Vertex coordinates[edit | edit source]

A retrograde pentagonal cuploid of edge length 1 has vertices given by the following coordinates:

## Related polyhedra[edit | edit source]

The retrograde pentagonal cuploid can be edge-inscribed into the small ditrigonary icosidodecahedron; it uses triangles and pentagons of the great ditrigonary icosidodecahedron as well as squares of the rhombihedron, the inscribed compound of 5 cubes.

## External links[edit | edit source]

- Klitzing, Richard. "rapescu".

- Wikipedia Contributors. "Crossed pentagonal cuploid".
- Webb, Robert. "Crossed Pentagonal Cuploid".