# Toroidal blend of 38 octahedra

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Toroidal blend of 38 octahedra | |
---|---|

Rank | 3 |

Type | Stewart toroid |

Elements | |

Faces | 8+8+24+24+24+24+48+48 triangles |

Edges | 24+24+24+24+24+48+48+48+48 |

Vertices | 6+6+24+24+24 |

Vertex figures | 6 squares, edge length 1 |

6 (3.3.3)^{4} | |

24 (3.3.3)^{2} | |

24 (3.3.3.3)^{2} (reflection-symmetric) | |

24 (3.3.3.3)^{2} (rectangular-symmetric) | |

Measures (edge length 1) | |

Volume | |

Surface area | |

Central density | 0 |

Related polytopes | |

Convex hull | Chamfered octahedron |

Abstract & topological properties | |

Flag count | 1248 |

Euler characteristic | –20 |

Orientable | Yes |

Genus | 11 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | No |

Nature | Tame |

The **toroidal blend of 38 octahedra** is a Stewart toroid that consists of 208 triangles. It can be obtained by outer-blending thirty-eight octahedra together in eight-membered loops that resemble rhombi, forming a virtual rhombic dodecahedron. The 14 octahedra at the virtual polyhedron's vertices are all oriented in the same way; the other 24 serve as triangular antiprisms.

## Relations[edit | edit source]

The toroid can be made out of copies of most other Platonic, Archimedean, or Johnson solids that share the faceplanes of the octahedron, including the icosahedron and some of its truncations.

## Gallery[edit | edit source]

## External links[edit | edit source]

- Doskey, Alex. "Chapter 7 - Exploration of (R)(A) Toroids".