# Snub dodecahedral antiprism

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Snub dodecahedral antiprism | |
---|---|

File:Snub dodecahedral antiprism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Sniddap |

Coxeter diagram | s2s5s3s ( |

Elements | |

Cells | 120 irregular tetrahedra, 30 rhombic disphenoids, 20 triangular gyroprisms, 12 pentagonal gyroprisms, 2 snub dodecahedra |

Faces | 120+120+120+120 scalene triangles, 40 triangles, 24 pentagons |

Edges | 60+60+60+60+120+120 |

Vertices | 120 |

Vertex figure | Triangular-pentagonal gyrowedge |

Measures (as derived from unit-edge great rhombicosidodecahedral prism) | |

Edge lengths | Diagonals of original squares (60+60+60+60): |

Edges of equilateral triangles (120): | |

Edges of pentagons (120): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Sniddap |

Regiment | Sniddap |

Dual | Pentagonal hexecontahedral antitegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (H_{3}×A_{1})+, order 120 |

Convex | Yes |

Nature | Tame |

The **snub dodecahedral antiprism**, **omnisnub dodecahedral antiprism**, or **sniddap**, also known as the **alternated great rhombicosidodecahedral prism**, is a convex isogonal polychoron that consists of 2 snub dodecahedra, 12 pentagonal gyroprisms, 20 triangular gyroprisms, 30 rhombic disphenoids, and 120 irregular tetrahedra. 4 tetrahedra and one of each other type of cell join at each vertex. It can be obtained through the process of alternating the great rhombicosidodecahedral prism. However, it cannot be made uniform, as it generally has 6 edge lengths, which can be minimized to no fewer than 3 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.12815.

## External links[edit | edit source]

- Klitzing, Richard. "sniddap".

- Wikipedia Contributors. "Omnisnub dodecahedral antiprism".