# Pyritosnub tesseract

Pyritosnub tesseract | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Pysnet |

Coxeter diagram | x4s3s3s () |

Elements | |

Cells | 96 skewed wedges, 32 triangular prisms, 24 rectangular trapezoprisms, 16 snub tetrahedra, 8 pyritosnub cubes |

Faces | 192 scalene triangles, 64+64 triangles, 96+96 isosceles trapezoids, 48+96 rectangles |

Edges | 96+96+96+192+192 |

Vertices | 192 |

Vertex figure | Polyhedron with 1 pentagon, 1 tetragon, and 5 triangles |

Measures (as derived from unit-edge great disprismatotesseractihexadecachoron) | |

Edge lengths | Remaining edges from class being alternated (96): 1 |

Edges from diagonals of original squares (96): | |

Edges of equilateral triangles (192+192): | |

Long edges of rectangles (96): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Pysnet |

Regiment | Pysnet |

Dual | Heptahedral hecatonenneacontadichoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{4}/2, order 192 |

Convex | Yes |

Nature | Tame |

The **pyritosnub tesseract** or **pysnet**, also known as the **edge-snub hexadecachoron**, is a convex isogonal polychoron that consists of 8 pyritosnub cubes, 16 snub tetrahedra, 24 rectangular trapezoprisms, 32 triangular prisms, and 96 skewed wedges. 3 wedges and one of each of the other 4 types of cells join at each vertex. It can be obtained through the process of alternating one set of 192 edges of the great disprismatotesseractihexadecachoron in such a way that the octagonal faces turn into rectangles. However, it cannot be made uniform, as it generally has 5 different edge lengths, which can be minimized to no more than 2 different sizes.

A variant with 8 regular icosahedra and 32 uniform triangular prisms can be vertex-inscribed into a prismatorhombisnub icositetrachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:*a* ≈ 1:1.49032, where *a* is the second largest real root of 37x^{6}-50x^{5}-81x^{4}+40x^{3}+80x^{2}+32x+4.

## Vertex coordinates[edit | edit source]

Vertex coordinates for a pyritosnub tesseract, created from the vertices of a great disprismatotesseractihexadecachoron of edge length 1, are given by all even permutations of:

A variant using regular icosahedra and uniform triangular prisms of edge length 1, centered at the origin, has vertices given by all even permutations of:

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by all even permutations of:

where

## External links[edit | edit source]

- Bowers, Jonathan. "Tessic Isogonals".

- Klitzing, Richard. "pysnet".
- Wikipedia contributors. "Bialternatosnub 16-cell".