# Pentagrammic prism

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Pentagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Stip |

Coxeter diagram | x x5/2o () |

Elements | |

Faces | 5 squares, 2 pentagrams |

Edges | 5+10 |

Vertices | 10 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–5/2: 90° |

4–4: 36° | |

Height | 1 |

Central density | 2 |

Number of external pieces | 12 |

Level of complexity | 6 |

Related polytopes | |

Army | Semi-uniform Pip, edge lengths (base), 1 (sides) |

Regiment | Stip |

Dual | Pentagrammic tegum |

Conjugate | Pentagonal prism |

Convex core | Pentagonal prism |

Abstract & topological properties | |

Flag count | 60 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | H_{2}×A_{1}, order 20 |

Convex | No |

Nature | Tame |

The **pentagrammic prism**, or **stip**, is a prismatic uniform polyhedron. It consists of 2 pentagrams and 5 squares. Each vertex joins one pentagram and two squares. As the name suggests, it is a prism based on a pentagram.

## Vertex coordinates[edit | edit source]

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

## Related polyhedra[edit | edit source]

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

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

## External links[edit | edit source]

- Klitzing, Richard. "stip".
- Wikipedia contributors. "Pentagrammic prism".
- McCooey, David. "Pentagrammic Prism"