# Brick-symmetric great icosahedron faceting

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Brick-symmetric great icosahedron faceting | |
---|---|

Rank | 3 |

Type | Orbiform |

Notation | |

Bowers style acronym | Bisgif |

Elements | |

Faces | 4+4 triangles, 4 pentagrams |

Edges | 2+2+2+8+8 |

Vertices | 4+4+4 |

Vertex figures | 4 nonconvex pentagons, edge lengths 1, 1, (√5–1)/2, 1, (√5–1)/2 |

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

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5/2-5/2: |

3-5/2 #1: | |

3-3: | |

3-5/2 #2: | |

Number of external pieces | 52 |

Level of complexity | 47 |

Related polytopes | |

Conjugate | Brick-symmetric icosahedron faceting |

Convex hull | Icosahedron, edge length (√5–1)/2 |

Convex core | Digonal orthobicupola |

Abstract & topological properties | |

Flag count | 88 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{3}, order 8 |

Convex | No |

Nature | Tame |

The **brick-symmetric great icosahedron faceting**, or **bisgif** is an orbiform polyhedron. It consists of 8 triangles and 4 pentagrams. As its name suggests, it is a faceting of the great icosahedron, and thus also of the small stellated dodecahedron.

It appears as a cell of the great digonal swirlprism.

## Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the small stellated dodecahedron.

## Gallery[edit | edit source]

## External links[edit | edit source]

- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#14 under sissid).