# Decagrammic prism

Jump to navigation
Jump to search

Decagrammic prism | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Stiddip |

Coxeter diagram | x x10/3o () |

Elements | |

Faces | 10 squares, 2 decagrams |

Edges | 10+20 |

Vertices | 20 |

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

Measures (edge length 1) | |

Circumradius | |

Volume | |

Dihedral angles | 4–10/3: 90° |

4–4: 72° | |

Height | 1 |

Central density | 3 |

Number of external pieces | 22 |

Level of complexity | 6 |

Related polytopes | |

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

Regiment | Stiddip |

Dual | Decagrammic tegum |

Conjugate | Decagonal prism |

Convex core | Decagonal prism |

Abstract & topological properties | |

Flag count | 120 |

Euler characteristic | 2 |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | I_{2}(10)×A_{1}, order 40 |

Convex | No |

Nature | Tame |

The **decagrammic prism**, or **stiddip**, is a prismatic uniform polyhedron. It consists of 2 decagrams and 10 squares. Each vertex joins one decagram and two squares. As the name suggests, it is a prism based on a decagram.

## Vertex coordinates[edit | edit source]

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

## Representations[edit | edit source]

A decagrammic prism has the following Coxeter diagrams:

- x x10/3o (full symmetry)
- x x5/3x (base with H2 symmetry)

## Related polyhedra[edit | edit source]

The great rhombisnub dodecahedron is a uniform polyhedron compound composed of 6 decagrammic prisms.

## External links[edit | edit source]

- Klitzing, Richard. "stiddip".
- Wikipedia contributors. "Decagrammic prism".