# Hexagonal-decagrammic duoprism

The **hexagonal-decagramic duoprism**, also known as **histadedip** or the **6-10/3 duoprism**, is a uniform duoprism that consists of 10 hexagonal prisms and 6 decagrammic prisms, with 2 of each meeting at each vertex.

Hexagonal-decagrammic duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Histadedip |

Info | |

Coxeter diagram | x6o x10/3o |

Symmetry | G2×I2(10), order 240 |

Army | Semi-uniform hadedip |

Regiment | Histadedip |

Elements | |

Vertex figure | Digonal disphenoid, edge lengths √3 (base 1), √(5–√5)/2 (base 2), √2 (sides) |

Cells | 10 hexagonal prisms, 6 decagrammic prisms |

Faces | 60 squares, 10 hexagons, 6 decagrams |

Edges | 60+60 |

Vertices | 60 |

Measures (edge length 1) | |

Circumradius | √(5–√5)/2 ≈ 1.17557 |

Hypervolume | 15√3(5–2√5)/4 ≈ 4.71903 |

Dichoral angles | Hip–6–hip: 72° |

Stiddip–10/3–stiddip: 120° | |

Hip–4–stiddip: 90° | |

Central density | 3 |

Related polytopes | |

Dual | Hexagonal-decagrammic duotegum |

Conjugate | Hexagonal-decagonal duoprism |

Properties | |

Convex | No |

Orientable | Yes |

Nature | Tame |

## Vertex coordinatesEdit

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

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

## External linksEdit

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

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