# Small ditrigonary icosidodecahedral prism

Small ditrigonary icosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sidtiddip |

Coxeter diagram | x x5/2o3o3*b () |

Elements | |

Cells | 20 triangular prisms, 12 pentagrammic prisms, 2 small ditrigonary icosidodecahedra |

Faces | 40 triangles, 60 squares, 24 pentagrams |

Edges | 20+120 |

Vertices | 40 |

Vertex figure | ditrigonal pyramid, edge lengths 1, (√5–1)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | 1 |

Hypervolume | |

Dichoral angles | Trip–4–stip: |

Sidtid–3–trip: 90° | |

Sidtid–5/2–stip: 90° | |

Height | 1 |

Central density | 2 |

Number of pieces | 74 |

Related polytopes | |

Army | Semi-uniform Dope |

Regiment | Sidtiddip |

Dual | Small triambic icosahedral tegum |

Conjugate | Great ditrigonary icosidodecahedral prism |

Abstract properties | |

Euler characteristic | –10 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **small ditrigonary icosidodecahedral prism** or **sidtiddip**, is a prismatic uniform polychoron that consists of 2 small ditrigonary icosidodecahedra, 12 pentagrammic prisms, and 20 triangular prisms. Each vertex joins 1 small ditrigonary icosidodecahedron, 3 pentagrammic prisms, and 3 triangular prisms. As the name suggests, it is a prism based on the small ditrigonary icosidodecahedron.

The small ditrigonary icosidodecahedral prism can be vertex-inscribed into the small stellated hecatonicosachoron.

## Vertex coordinates[edit | edit source]

The vertices of a small ditrigonary icosidodecahedral prism of edge length 1 are given by all permutations and changes of sign of the first three coordinates of:

along with all even permutations and all sign changes of:

The first set of vertices are those of an inscribed tesseract, seen as a cubic prism.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#920).

- Klitzing, Richard. "sidtiddip".