# Augmented sphenocorona

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Augmented sphenocorona | |
---|---|

Rank | 3 |

Type | CRF |

Notation | |

Bowers style acronym | Auwaco |

Elements | |

Faces | 1+1+1+1+2+2+2+2+2+2 triangles, 1 square |

Edges | 1+1+1+1+2+2+2+2+2+2+2+2+2+2+2 |

Vertices | 1+1+1+2+2+2+2 |

Vertex figures | 1+1+2+2 pentagons, edge length 1 |

2 trapezoids, edge lengths 1, 1, 1, √2 | |

2 irregular pentagons, edge lengths 1, 1, 1, 1, √2 | |

1 square, edge length 1 | |

Measures (edge length 1) | |

Volume | |

Central density | 1 |

Number of external pieces | 17 |

Level of complexity | 52 |

Related polytopes | |

Army | Auwaco |

Regiment | Auwaco |

Dual | Order-4 monotruncated order-5 truncated bi-apiculated tetrahedron |

Conjugate | Augmented sphenocorona |

Abstract & topological properties | |

Flag count | 104 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | A_{1}×I×I, order 2 |

Convex | Yes |

Nature | Tame |

The **augmented sphenocorona** is one of the 92 Johnson solids (J_{87}). It consists of 1+1+1+1+2+2+2+2+2+2 triangles and 1 square. It can be constructed by attaching a square pyramid to one of the square faces of the sphenocorona.

## Coordinates[edit | edit source]

Coordinates for the vertices of an sphenocorona with unit edge length are given by:

- ,
- ,
- ,
- ,
- .

where k ≈ 0.85273 is the smallest positive root of the quartic polynomial:

This root can also be given as:

## External links[edit | edit source]

- Klitzing, Richard. "auwaco".
- Quickfur. "The Augmented Sphenocorona".

- Wikipedia contributors. "Augmented sphenocorona".
- McCooey, David. "Augmented Sphenocorona"