# Small supersemicupola

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Small supersemicupola | |
---|---|

Rank | 3 |

Type | Acrohedron, orbiform |

Elements | |

Faces | 7+7 triangles, 7 heptagons, 1 heptagram |

Edges | 7+7+7+14+14 |

Vertices | 7+7+7+7 |

Related polytopes | |

Conjugate | Great supersemicupola |

Abstract & topological properties | |

Flag count | 196 |

Euler characteristic | 1 |

Orientable | No |

Genus | 1 |

Properties | |

Symmetry | I_{2}(7)×I, order 14 |

Flag orbits | 14 |

Convex | No |

Nature | Tame |

The **small supersemicupola** is the first known example of a 7-7-3 acrohedron, i.e. a polyhedron with all regular faces that has two heptagons and a triangle meeting at a vertex. It was discovered by Mason Green in 2005 along with the great supersemicupola, a 7/2-7/2-3 acrohedron. Most acrons containing heptagons have no known acrohedron, so the existence of a 7-7-3 acrohedron is rather unusual.

As the name suggests, the small supersemicupola bears similarities to a heptagrammic semicupola (cuploid). Like the semicupolae, it is non-orientable.

The shape is part of a larger family of regular-faced polyhedra formed using Green's rules.

## External links[edit | edit source]

- Jim McNeill. "7-7-3."
- Jim McNeill. "n-n-3 acrohedra."
- Green, Mason. "Geometry". Archived from the original on 2008-10-14.