# Semicupolaically-faceted great icosahedron

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Semicupolaically-faceted great icosahedron | |
---|---|

Rank | 3 |

Type | Orbiform |

Notation | |

Bowers style acronym | Scufgi |

Elements | |

Faces | 1+6 triangles, 3 pentagrams |

Edges | 3+3+6+6 |

Vertices | 3+3+3 |

Vertex figures | 3 nonconvex pentagons, edge lengths 1, 1, (√5–1)/2, 1, (√5–1)/2 |

3 butterflies, edge lengths 1 and (√5–1)/2 | |

3 isosceles triangles, edge lengths 1, 1, (√5–1)/2 | |

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 3-5/2: |

3-3: | |

Related polytopes | |

Army | Teddi, edge length |

Conjugate | Semicupolaically-faceted icosahedron |

Abstract & topological properties | |

Flag count | 72 |

Euler characteristic | 1 |

Orientable | No |

Genus | 1 |

Properties | |

Symmetry | A_{2}×I, order 6 |

Convex | No |

Nature | Tame |

The **semicupolaically-faceted great icosahedron**, or **scufgi**, is an orbiform polyhedron. It consists of 7 triangles and 3 pentagrams. As its name suggests, it is a faceting of the great icosahedron, and thus also of the small stellated dodecahedron. It can also be obtained by blending together three pentagrammic pyramids, the three of them all sharing a triangle.

It appears as a cell of the disnub disicositetrachoron.

## Vertex coordinates[edit | edit source]

The vertices of a semicupolaically-faceted great icosahedron of edge length 1 are given by:

and all sign changes of none or one of the nonzero coordinates of:

## Gallery[edit | edit source]

## External links[edit | edit source]

- Klitzing, Richard. "scufgi".
- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#12 under sissid).