# Hollow small stellated dodecahedral antiprism

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Hollow small stellated dodecahedral antiprism | |
---|---|

Rank | 4 |

Type | Scaliform |

Space | Spherical |

Notation | |

Bowers style acronym | Hossdap |

Coxeter diagram | ß2ß5o5/2o (hossdap + 2 degenerate cells) |

Elements | |

Cells | 24 pentagrammic pyramids, 12 pentagrammic antiprisms |

Faces | 120 triangles, 24 pentagrams |

Edges | 60+60 |

Vertices | 24 |

Vertex figure | Pentagrammic cuploid, edge lengths (√5–1)/2 (pentagon), 1 (pentagram), 1 (lateral edges) |

Measures (edge length 1) | |

Circumradius | |

Height | |

Related polytopes | |

Army | Semi-uniform Ipe |

Regiment | Hossdap |

Dual | Hollow great dodecahedral antitegum |

Convex core | Elongated dodecahedral tegum |

Topological properties | |

Orientable | No |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **hollow small stellated dodecahedral antiprism** or **hossdap** is a prismatic scaliform polychoron that consists of 12 pentagrammic antiprisms and 24 pentagrammic pyramids. 5 pentagrammic antiprisms and 6 pentagrammic pyramids join at each vertex.

It can be constructed as a holosnub great dodecahedral prism after coinciding base cells blend out.

## Vertex coordinates[edit | edit source]

The vertices of a hollow small stellated dodecahedral antiprism of edge length 1 are given by all even permutations of the first three coordinates of:

## Convex core[edit | edit source]

The convex core of this polychoron is an **elongated dodecahedral tegum** that consists of 12 pentagonal prisms (from the stap cells) and 24 pentagonal pyramids (from the stappy cells).

## External links[edit | edit source]

- Bowers, Jonathan. "Category S1: Simple Scaliforms" (#S2).

- Klitzing, Richard. "hossdap".