# Pyritosnub cube

Pyritosnub cube | |
---|---|

Rank | 3 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Pysnic |

Coxeter diagram | |

Elements | |

Faces | 8 triangles, 12 isosceles trapezoids, 6 rectangles |

Edges | 12+12+24 |

Vertices | 24 |

Vertex figure | Irregular tetragon |

Measures (edge length 1) | |

Central density | 1 |

Related polytopes | |

Army | Pysnic |

Regiment | Pysnic |

Dual | Tetragonal icositetrahedron |

Abstract properties | |

Euler characteristic | 2 |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{3}/2, order 24 |

Convex | Yes |

Nature | Tame |

The **pyritosnub cube**, or **pysnic**, is a convex isogonal polyhedron that is a variant of the small rhombicuboctahedron with pyritohedral symmetry. It has 8 equilateral triangles, 6 rectangles, and 12 isosceles trapezoids for faces.

It can generally be formed by alternating one set of 24 edges of a general great rhombicuboctahedron, such that the octagons become long rectangles.

This polyhedron generally has 3 types of edges, as the 24 edges of the small rhombicuboctahedron's squares split into 2 groups of 12, turning the squares into rectangles.

The variant derived from the uniform great rhombicuboctahedron has rectangles with edge lengths 1 and and triangles of side .

Another case of this polyhedron, with 6 golden rectangles, can be obtained by removing the 6 vertices of an inscribed octahedron from a uniform icosidodecahedron.

The Conway-Thurston symbol for this is 3x * x2x, the first 'x' represents the triangle, and the other two x's are for the rectangle.

## Vertex coordinates[edit | edit source]

A pyritosnub cube with edges of length a (long edge of rectangle), b (short edge of rectangle), and c (triangle-trapezoid) has vertex coordinates given by all cyclic permutations of:

## External links[edit | edit source]

- Klitzing, Richard. "pysnic".