# Small icosicosidodecahedral alterprism

The **small icosicosidodecahedral alterprism**, **small icosicosidodecahedral cupoliprism**, or **siidcup**, is a scaliform polychoron. It consists of two small icosicosidodecahedra as bases, joined by 12 pentagrammic antiprisms and 40 triangular cupolae. 1 small icosicosidodecahedron, 1 pentagrammic antiprism, and 3 triangular cupolae join at each vertex. It can be formed by alternated faceting of the rhombicosidodecahedral prism. It can also be formed by partial Stott expansion of the small ditrigonary icosidodecahedral alterprism, expanding to .

Small icosicosidodecahedral alterprism | |
---|---|

Rank | 4 |

Type | Scaliform |

Space | Spherical |

Notation | |

Bowers style acronym | Siida (also Siidcup) |

Coxeter diagram | |

Elements | |

Cells | 2 small icosicosidodecahedra, 12 pentagrammic antiprisms, 40 triangular cupolae |

Faces | 40+120 triangles, 60 squares, 24 pentagrams, 40 hexagons |

Edges | 120+120+120 |

Vertices | 120 |

Vertex figure | Skewed wedge |

Measures (edge length 1) | |

Circumradius | |

Height | |

Number of external pieces | 174 |

Related polytopes | |

Army | Semi-uniform sriddip |

Regiment | Siidcup |

Conjugate | No real conjugate |

Abstract & topological properties | |

Orientable | Yes |

Properties | |

Symmetry | H3×A1, order 240 |

Convex | No |

Nature | Tame |

It is also a segmentochoron, as siid atop siid.

## External linksEdit

- Bowers, Jonathan. "Category S1: Simple Scaliforms" (#S3).

- Klitzing, Richard. "siidcup".