# Snub prismatotriacontaditeron

Snub prismatotriacontaditeron | |
---|---|

File:Snub prismatotriacontaditeron.png | |

Rank | 5 |

Type | Isogonal |

Notation | |

Bowers style acronym | Snippit |

Coxeter diagram | s3s3s3s4o |

Elements | |

Tera | 960 sphenoidal pyramids, 80 digonal-triangular duoantiprisms, 40 pyritohedral icosahedral antiprisms, 32 snub pentachora, 10 snub rhombatohexadecachora |

Cells | 1920 irregular tetrahedra, 960+960+960 sphenoids, 240+240 tetragonal disphenoids, 80+160 snub tetrahedra, 80 pyritohedral icosahedra, 320+320 triangular gyroprisms |

Faces | 1920+1920+1920 scalene triangles, 960+960+960+960 isosceles triangles, 320+320+640 triangles |

Edges | 480+480+960+960+960+960+1920 |

Vertices | 960 |

Measures (based on uniform great prismated triacontaditeron of edge length 1) | |

Edge lengths | Diagonals of squares (480+480+960+960): |

Edges of triangles (960+960+1920): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Dual | Tetradecachoric enneacosihexecontateron |

Abstract & topological properties | |

Euler characteristic | 2 |

Orientable | Yes |

Properties | |

Symmetry | B_{5}/2, order 1920 |

Convex | Yes |

Nature | Tame |

The **snub prismatotriacontaditeron** or **snippit**, also commonly called the **omnisnub demipenteract**, is a convex isogonal polyteron that consists of 10 snub rhombatohexadecachora, 32 snub pentachora, 40 pyritohedral icosahedral antiprisms, 80 digonal-triangular duoantiprisms, and 960 sphenoidal pyramids. 1 snub rhombatohexadecachoron, 2 snub pentachora, 1 pyritohedral icosahedral antiprism, 1 digonal-triangular duoantiprism, and 5 sphenoidal pyramids join at each vertex. It can be obtained through the process of alternating the great prismated triacontaditeron. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.21301.

## Vertex coordinates[edit | edit source]

The vertices of a snub prismatotriacontaditeron, assuming that the edge length differences are minimized via the absolute value method, centered at the origin, are given by all even permutations and all sign changes of:

Another set of coordinates for a snub prismatotriacontaditeron, using the ratio method, centered at the origin, are given by all even permutations and all sign changes of:

## External links[edit | edit source]

- Wikipedia contributors. "Snub 5-demicube".
- Klitzing, Richard. "Snippit".