# Octagrammic prism

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Octagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Stop |

Coxeter diagram | x x8/3o () |

Elements | |

Faces | 8 squares, 2 octagrams |

Edges | 8+16 |

Vertices | 16 |

Vertex figure | Isosceles triangle, edge lengths √2–√2, √2, √2 |

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–8/3: 90° |

4–4: 45° | |

Height | 1 |

Central density | 3 |

Number of external pieces | 18 |

Level of complexity | 6 |

Related polytopes | |

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

Regiment | Stop |

Dual | Octagrammic tegum |

Conjugate | Octagonal prism |

Convex core | Octagonal prism |

Abstract & topological properties | |

Flag count | 96 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(8)×A_{1}, order 32 |

Convex | No |

Nature | Tame |

The **octagrammic prism**, or **stop**, is a prismatic uniform polyhedron. It consists of 2 octagrams and 8 squares. Each vertex joins one octagram and two squares. As the name suggests, it is a prism based on an octagram.

Similar to how an octagonal prism can be vertex-inscribed into the small rhombicuboctahedron, an octagrammic prism can be vertex inscribed into the quasirhombicuboctahedron.

## Vertex coordinates[edit | edit source]

An octagrammic prism of edge length 1 has vertex coordinates given by:

## Representations[edit | edit source]

An octagrammic prism has the following Coxeter diagrams:

- x x8/3o (full symmetry)
- x x4/3x (base has BC2 symmetry)

## External links[edit | edit source]

- Klitzing, Richard. "stop".
- Wikipedia contributors. "Octagrammic prism".
- McCooey, David. "Octagrammic Prism"