# Pentagrammic antiprism

The **pentagrammic antiprism**, or **stap**, is a prismatic uniform polyhedron. It consists of 10 triangles and 2 pentagrams. Each vertex joins one pentagram and three triangles. As the name suggests, it is an antiprism based on a pentagram. It is one of two pentagrammic antiprisms, the other one being the pentagrammic retroprism. In this case, the pentagrams are aligned with one another.

Pentagrammic antiprism | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Stap |

Coxeter diagram | s2s10/2o () |

Elements | |

Faces | 10 triangles, 2 pentagrams |

Edges | 10+10 |

Vertices | 10 |

Vertex figure | Isosceles trapezoid, edge lengths 1, 1, 1, (√5–1)/2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 5/2–3: |

3–3: | |

Height | |

Central density | 2 |

Number of external pieces | 32 |

Level of complexity | 11 |

Related polytopes | |

Army | Semi-uniform Pip |

Regiment | Stap |

Dual | Pentagrammic antitegum |

Conjugate | Pentagonal retroprism |

Convex core | Pentagonal bifrustum |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{2}×A_{1}, order 20 |

Convex | No |

Nature | Tame |

## Vertex coordinatesEdit

A pentagrammic antiprism of edge length 1 has vertex coordinates given by:

## Related polyhedraEdit

Two non-prismatic uniform polyhedron compounds are composed of pentagrammic antiprisms:

There are an infinite amount of prismatic uniform compounds that are the antiprisms of compounds of pentagrams.

## In vertex figuresEdit

Pentagrammic antiprisms appear as vertex figures of four uniform polychora: the small prismatohecatonicosachoron, pentagrammal antiprismatoverted hexacosihecatonicosachoron, small pentagrammal antiprismatoverted dishecatonicosachoron, and great pentagrammal antiprismatoverted dishecatonicosachoron.

## External linksEdit

- Klitzing, Richard. "stap".

- Wikipedia Contributors. "Pentagrammic antiprism".
- McCooey, David. "Pentagrammic Antiprism"