# Prismatorhombisnub icositetrachoron

Prismatorhombisnub icositetrachoron | |
---|---|

Rank | 4 |

Type | Scaliform |

Space | Spherical |

Notation | |

Bowers style acronym | Prissi |

Coxeter diagram | s3s4o3x () |

Elements | |

Cells | 96 triangular cupolas, 96 triangular prisms, 24 truncated tetrahedra, 24 icosahedra |

Faces | 96+192+288 triangles, 288 squares, 96 hexagons |

Edges | 144+288+576 |

Vertices | 288 |

Vertex figure | Digonal-pentagonal wedge, pentagon edge length 1, other lateral edge lengths 1, √2, and √3 |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–tricu: |

Tut–3–tricu: | |

Tut–6–tricu: | |

Ike–3–trip: 150° | |

Ike–3–tricu: | |

Central density | 1 |

Related polytopes | |

Army | Prissi |

Regiment | Prissi |

Dual | Dipentanotched diacosioctacontoctachoron |

Conjugate | Prismatorhombiretrosnub icositetrachoron |

Abstract properties | |

Euler characteristic | 0 |

Topological properties | |

Orientable | Yes |

Properties | |

Symmetry | F_{4}/2, order 576 |

Convex | Yes |

Nature | Tame |

The **prismatorhombisnub icositetrachoron**, or **prissi**, is a convex scaliform polychoron. It consists of 96 triangular prisms, 96 triangular cupolas, 24 truncated tetrahedra, and 24 icosahedra. 1 icosahedron, 1 truncated tetrahedron, 2 triangular prisms, and 3 triangular cupolas join at each vertex.

It can be constructed from the snub disicositetrachoron by expanding the icosahedral cells outward by unit distance, or from the prismatorhombated icositetrachoron by alternating the triangles and equalizing edge lengths. It is also a subsymmetrical faceting of the prismatodishecatonicosachoron.

It contains the vertices of a pyritosnub tesseract with regular icosahedra and uniform triangular prisms.

## Vertex coordinates[edit | edit source]

A prismatorhombisnub icositetrachoron of edge length 1 has vertex coordinates given by all even permutations of:

## Representations[edit | edit source]

A prismatorhombisnub icositetrachoron has the following Coxeter diagrams:

- s3s4o3x (full symmetry)
- fox3xxx3xfo *b3oxf&#zx (D4 symmetry)

## External links[edit | edit source]

- Bowers, Jonathan. "Category S3: Special Scaliforms" (#S30).

- Klitzing, Richard. "prissi".

- Quickfur. "The Runcinated Snub 24-cell".

- Hi.gher.Space Wiki Contributors. "Runcinated snub demitesseract".

- Wikipedia Contributors. "Runcic snub 24-cell".