# Snub dodecahedral prism

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Snub dodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sniddip |

Coxeter diagram | x2s5s3s () |

Elements | |

Cells | 20+60 triangular prisms, 12 pentagonal prisms, 2 snub dodecahedra |

Faces | 40+120 triangles, 30+60+60 squares, 24 pentagons |

Edges | 60+60+120+120 |

Vertices | 120 |

Vertex figure | Mirror-symmetric (topologically irregular) pentagonal pyramid, edge lengths 1, 1, 1, 1, (1+√5)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | ≈ 2.21306 |

Hypervolume | ≈ 37.61665 |

Dichoral angles | Trip–4–trip: ≈ 164.17537° |

Trip–4–pip: ≈ 152.92992° | |

Snid–5–pip: 90° | |

Snid–3–trip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 94 |

Level of complexity | 20 |

Related polytopes | |

Army | Sniddip |

Regiment | Sniddip |

Dual | Pentagonal hexecontahedral tegum |

Conjugates | Great snub icosidodecahedral prism, great inverted snub icosidodecahedral prism, great inverted retrosnub icosidodecahedral prism |

Abstract & topological properties | |

Flag count | 4800 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}+×A_{1}, order 120 |

Convex | Yes |

Nature | Tame |

The **snub dodecahedral prism** or **sniddip** is a prismatic uniform polychoron that consists of 2 snub dodecahedra, 12 pentagonal prisms, and 20+60 triangular prisms. Each vertex joins 1 snub dodecahedron, 1 pentagonal prism, and 4 triangular prisms. It is a prism based on the snub dodecahedron. As such it is also a convex segmentochoron (designated K-4.110 on Richard Klitzing's list).

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The coordinates of a snub dodecahedral prism, centered at the origin and with unit edge length, are given by all even permutations with an odd number of sign changes of the first three coordinates of:

as well as all even permutations with an even number of sign changes of the first three coordinates of:

where

## External links[edit | edit source]

- Bowers, Jonathan. "Category 19: Prisms" (#952).

- Klitzing, Richard. "Sniddip".

- Wikipedia Contributors. "Snub dodecahedral prism".