# Pentagrammic pyramid

Jump to navigation
Jump to search

Pentagrammic pyramid | |
---|---|

Rank | 3 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Stappy |

Coxeter diagram | ox5/2oo&#x |

Elements | |

Faces | 5 triangles, 1 pentagram |

Edges | 5+5 |

Vertices | 1+5 |

Vertex figures | 1 pentagram, edge length 1 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 3-5/2: |

3-3: | |

Height | |

Related polytopes | |

Army | Non-RF peppy, edge lengths (base), 1 (sides) |

Regiment | Stappy |

Dual | Pentagrammic pyramid |

Conjugate | Pentagonal pyramid |

Convex core | Pentagonal pyramid |

Abstract & topological properties | |

Flag count | 40 |

Orientable | Yes |

Properties | |

Symmetry | H_{2}×I, order 10 |

Convex | No |

Nature | Tame |

The **pentagrammic pyramid**, or **stappy**, is a pyramid with a pentagrammic base and 5 triangles as sides.

It is the vertex-first cap of the great icosahedron. A regular great icosahedron can be constructed by attaching two pentagrammic pyramids to the bases of a pentagrammic retroprism.

## Vertex coordinates[edit | edit source]

A pentagrammic pyramid of edge length 1 has the following vertices:

## Related polyhedra[edit | edit source]

Two pentagrammic pyramids can be attached at their bases to form a pentagrammic tegum.

## External links[edit | edit source]

- Bowers, Jonathan. "Batch 2: Ike and Sissid Facetings" (#4 under sissid).

- Klitzing, Richard. "stappy".
- Wikipedia contributors. "Pentagrammic pyramid".