# Small inverted retrosnub icosicosidodecahedral prism

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Small inverted retrosnub icosicosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sirsiddip |

Coxeter diagram | x2s5/2s3/2s3/2*b () |

Elements | |

Cells | 60 triangular prisms, 40 triangular prisms as 20 hexagrammic prisms, 12 pentagrammic prisms, 2 small inverted retrosnub icosicosidodecahedra |

Faces | 120 triangles, 80 triangles as 40 hexagrams, 60+60+60 squares, 24 pentagrams |

Edges | 60+120+120+120 |

Vertices | 120 |

Vertex figure | Mirror-symmetric hexagonal pyramid, edge lengths 1, 1, 1, 1, 1, (√5–1)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Sirsid–5/2–stip: 90° |

Sirsid–3–trip: 90° | |

Stip–4–trip: | |

Trip–4–trip: | |

Height | 1 |

Central density | 38 |

Number of pieces | 3062 |

Related polytopes | |

Army | Semi-uniform Tiddip |

Regiment | Sirsiddip |

Dual | Small hexagrammic hexecontahedral tegum |

Abstract properties | |

Euler characteristic | –30 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **small inverted retrosnub icosicosidodecahedral prism** or **sirsiddip** is a prismatic uniform polychoron that consists of 2 small inverted retrosnub icosicosidodecahedra, 12 pentagrammic prisms, and 40+60 triangular prisms (40 of which form compounds in the same hyperplane, with bases combining into hexagrams). Each vertex joins 1 small inverted retrosnub icosicosidodecahedron, 1 pentagrammic prism, and 5 triangular prisms. As the name suggests, it is a prism based on the small inverted retrosnub icosicosidodecahedron.

## Vertex coordinates[edit | edit source]

A small inverted retrosnub icosicosidodecahedral prism of edge length 1 has vertex coordinates given by all even permutations of the first three coordinates of:

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#961).

- Klitzing, Richard. "sirsiddip".