# Brick symmetric icosahedron faceting

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

Rank | 3 |

Type | Orbiform |

Notation | |

Bowers style acronym | Bissif |

Elements | |

Faces | 4+4 triangles, 4 pentagons |

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

Vertices | 4+4+4 |

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

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

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3-3: |

3-5 #1: | |

5-5: | |

3-5 #2: | |

Central density | 1 |

Number of external pieces | 16 |

Level of complexity | 13 |

Related polytopes | |

Conjugate | Brick-symmetric great icosahedron faceting |

Convex hull | Icosahedron |

Convex core | Digonal orthobicupola, oxo2xfx&#xt |

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 icosahedron faceting** or **bissif**, also called the **spaceship**, is an orbiform polyhedron. It consists of 8 triangles and 4 pentagons. As its name suggests, it is a faceting of the icosahedron.

It appears as a cell of the small digonal swirlprism.

## Vertex coordinates[edit | edit source]

Its vertex coordinates are the same as those of the icosahedron.

## External links[edit | edit source]

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