# Toroidal blend of 92 dodecahedra

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Toroidal blend of 92 dodecahedra | |
---|---|

Rank | 3 |

Type | Stewart toroid |

Elements | |

Faces | 12+12+60+60+60+60+60+60+120+120+120+120 pentagons |

Edges | 60+60+60+60+120 +60+60+60+60+120+120+120 +60+60+120+120+120+120+120+120+120+120+120 |

Vertices | 60+60+60+60 +20+20+60+60+120+120 +60+60+120+120+120+120 |

Vertex figures | 20+20+60+60+60+60+120+120+120+120 triangles, edge length (1+√5)/2 |

60+60+120+120 [5.5.5.5] | |

60+60 [5.5.5.5.5] | |

Measures (edge length 1) | |

Volume | |

Surface area | |

Central density | 0 |

Related polytopes | |

Convex hull | Chamfered dodecahedron, edge lengths 1 (pentagon), (hexagon-hexagon) |

Abstract & topological properties | |

Flag count | 8640 |

Euler characteristic | –56 |

Orientable | Yes |

Genus | 29 |

Properties | |

Symmetry | H_{3}, order 120 |

Convex | No |

Nature | Tame |

The **toroidal blend of 92 dodecahedra** is a Stewart toroid that consists of 864 pentagons. It can be obtained by outer-blending ninety-two dodecahedra together in eight-membered loops that resemble rhombi, forming a virtual rhombic triacontahedron. The thirty-two dodecahedra at the virtual polyhedron's vertices are all oriented in the same way.

## Relations[edit | edit source]

Versions of the toroid can be made out of copies of most Archimedean and Johnson solids that share the faceplanes of the dodecahedron.

## External links[edit | edit source]

- Doskey, Alex. "Chapter 7 - Exploration of (R)(A) Toroids".
- Miyazaki, Koji and Takada, Ichiro. "Uniform Ant-hills in the World of Golden Isozonohedra", figure 26(4)
- Parker, Matt. “Polygons of New York”.