# Small snubahedron

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Small snubahedron | |
---|---|

Rank | 3 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sis |

Elements | |

Components | 6 tetrahedra |

Faces | 24 triangles |

Edges | 12+24 |

Vertices | 24 |

Vertex figure | Equilateral triangle, edge length 1 |

Measures (edge length 1) | |

Circumradius | |

Inradius | |

Volume | |

Dihedral angle | |

Central density | 6 |

Related polytopes | |

Army | Semi-uniform Toe |

Regiment | Sis |

Dual | Small snubahedron |

Conjugate | Small snubahedron |

Abstract & topological properties | |

Schläfli type | {3,3} |

Orientable | Yes |

Properties | |

Symmetry | A_{3}, order 24 |

Convex | No |

Nature | Tame |

The **small snubahedron**, **sis**, or **compound of six tetrahedra with rotational freedom** is a uniform polyhedron compound. It consists of 24 triangles, with three faces joining at a vertex.

This compound has rotational freedom, represented by an angle θ. At θ = 0°, all six tetrahedra coincide. We rotate these tetrahedra around their 2-fold axes of symmetry (2 each), seeing them as digonal antiprisms. At θ = 45° the compound has double symmetry resulting in the snubahedron.

This compound can be formed by taking one of the tetrahedra inscribed in each cube of the rhombisnub dishexahedron.

## Vertex coordinates[edit | edit source]

The vertices of a small snubahedron of edge length 1 and rotation angle θ are given by all even permutations of:

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C5: Tets and Cubes" (#32).

- Klitzing, Richard. "sis".

- Wikipedia Contributors. "Compound of six tetrahedra with rotational freedom".