# Pentagonal-decagrammic duoprism

(Redirected from 5-10/3 duoprism)

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Pentagonal-decagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Pistadedip |

Info | |

Coxeter diagram | x5o x10/3o |

Symmetry | H2×I2(10), order 200 |

Army | Semi-uniform padedip |

Regiment | Pistadedip |

Elements | |

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

Cells | 10 pentagonal prisms, 5 decagrammic prisms |

Faces | 50 squares, 10 pentagons, 5 decagrams |

Edges | 50+50 |

Vertices | 50 |

Measures (edge length 1) | |

Circumradius | √2(5–√5)/5 ≈ 1.05146 |

Hypervolume | 25/8 = 3.125 |

Dichoral angles | Pip–5–pip: 72° |

Stiddip–10/3–stiddip: 108° | |

Pip–4–stiddip: 90° | |

Central density | 3 |

Related polytopes | |

Dual | Pentagonal-decagrammic duotegum |

Conjugates | Pentagonal-decagonal duoprism, Pentagrammic-decagonal duoprism, Pentagrammic-decagrammic duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

The **pentagonal-decagrammic duoprism**, also known as **pistadedip** or the **5-10/3 duoprism**, is a uniform duoprism that consists of 10 pentagonal prisms and 5 decagrammic prisms, with two of each meeting at each vertex.

## Vertex coordinates[edit | edit source]

The coordinates of a pentagonal-decagrammic duoprism, centered at the origin and with edge length 1, are given by:

- (±1/2, –√(5+2√5)/20, ±1/2, ±√(5–2√5)/2),
- (±1/2, –√(5+2√5)/20, ±(3–√5)/4, ±√(5–√5)/8),
- (±1/2, –√(5+2√5)/20, ±(√5–1)/2, 0),
- (±(1+√5)/4, √(5–√5)/40, ±1/2, ±√(5–2√5)/2),
- (±(1+√5)/4, √(5–√5)/40, ±(3–√5)/4, ±√(5–√5)/8),
- (±(1+√5)/4, √(5–√5)/40, ±(√5–1)/2, 0),
- (0, √(5+√5)/10, ±1/2, ±√(5–2√5)/2),
- (0, √(5+√5)/10, ±(3–√5)/4, ±√(5–√5)/8),
- (0, √(5+√5)/10, ±(√5–1)/2, 0).

## External links[edit | edit source]

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

- Klitzing, Richard. "Pistadedip".

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