# Pentagrammic prism

Jump to navigation
Jump to search

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

Rank | 3 |

Type | Uniform |

Space | Spherical |

Bowers style acronym | Stip |

Info | |

Coxeter diagram | x x5/2o |

Symmetry | H2×A1, order 20 |

Army | Semi-uniform Pip |

Regiment | Pip |

Elements | |

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

Faces | 5 squares, 2 pentagrams |

Edges | 5+10 |

Vertices | 10 |

Measures (edge length 1) | |

Circumradius | √(15–2√5)/20 ≈ 0.72553 |

Volume | √25–10√5/4 ≈ 0.40615 |

Dihedral angles | 4–5/2: 90° |

4–4: 36° | |

Height | 1 |

Central density | 2 |

Euler characteristic | 2 |

Related polytopes | |

Dual | Pentagrammic bipyramid |

Conjugate | Pentagonal prism |

Convex core | Pentagonal prism |

Properties | |

Convex | No |

Orientable | Yes |

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:

- (±1/2, –√(5–2√5)/20, ±1/2),
- (±(√5–1)/4, √(5+√5)/40, ±1/2),
- (0, –√(5–√5)/10, ±1/2).

## 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".