# Small ditrigonary icosidodecahedral antiprism

Small ditrigonary icosidodecahedral antiprism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sidtidap |

Coxeter diagram | β2β5o3o () |

Elements | |

Cells | 40 tetrahedra, 12 pentagrammic antiprisms, 2 small ditrigonary icosidodecahedra |

Faces | 40+120 triangles, 24 pentagrams |

Edges | 60+120 |

Vertices | 40 |

Vertex figure | Triangular cupola, edge lengths (√5–1)/2 (3 base edges), 1 (remaining edges) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–stap: |

Sidtid–3–tet: | |

Sidtid–5/2–stap: 90° | |

Height | |

Number of external pieces | 174 |

Level of complexity | 32 |

Related polytopes | |

Army | Semi-uniform Dope |

Regiment | Sidtidap |

Dual | Small triambic icosahedral antitegum |

Conjugate | None |

Abstract & topological properties | |

Euler characteristic | –10 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | No |

Nature | Tame |

The **small ditrigonary icosidodecahedral antiprism** or **sidtidap**, is a nonconvex uniform polychoron that consists of 2 small ditrigonary icosidodecahedra, 12 pentagrammic antiprisms, and 40 tetrahedra. Each vertex joins 1 small ditrigonary icosidodecahedron, 3 pentagrammic antiprisms, and 4 tetrahedra.

It can be obtained as a holosnub dodecahedral prism.

## Cross-sections[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a small ditrigonary icosidodecahedral antiprism of edge length 1 are given by:

along with all even permutations of the first three coordinates of:

## Related polychora[edit | edit source]

The regiment of the small ditrigonary icosidodecahedral antiprism also includes the ditrigonary dodecadodecahedral antiprism and the great ditrigonary icosidodecahedral antiprism.

The small icosicosidodecahedral alterprism is a partial Stott expansion of this polychoron.

## External links[edit | edit source]

- Bowers, Jonathan. "Category 20: Miscellaneous" (#966).

- Klitzing, Richard. "sidtidap".