# Stelladodecahedron cone

The **stelladodecahedron cone**, or **sadcone**, is a nonconvex orbiform polyhedron and an edge-faceting of the small stellated dodecahedron. Its faces are 5 pentagrams and 5 triangles. It is named as such because the 5 pentagrams are arranged around one vertex similar to the configuration found in the small stellated dodecahedron.

Stelladodecahedron cone | |
---|---|

Rank | 3 |

Notation | |

Bowers style acronym | Sadcone |

Elements | |

Faces | 5 triangles, 5 pentagrams |

Edges | 5+5+10 |

Vertices | 1+5+5 |

Vertex figures | 1 pentagon, edge length (√5–1)/2 |

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

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

Measures (edge length 1) | |

Circumradius | |

Dihedral angles | 5/2–5/2: |

3–5/2 #1: | |

3–5/2 #2: | |

Related polytopes | |

Army | Gyepip, edge length |

Regiment | Sadcone |

Conjugate | Great dodecahedron cone |

Convex hull | Gyroelongated pentagonal pyramid |

Abstract & topological properties | |

Flag count | 80 |

Euler characteristic | 1 |

Orientable | No |

Genus | 1 |

Properties | |

Symmetry | H_{2}×I, order 10 |

Convex | No |

Nature | Tame |

## Vertex coordinates edit

Its vertex coordinates are the same as those of the small stellated dodecahedron with any 1 vertex removed.

## External links edit

- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#5 under sissid).