# Compound of six tetrahedra

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Compound of six tetrahedra | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Snu |

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 |

Number of external pieces | 120 |

Level of complexity | 20 |

Related polytopes | |

Army | Semi-uniform Toe, edge lengths (squares), (between ditrigons) |

Regiment | Snu |

Dual | Compound of six tetrahedra |

Conjugate | Compound of six tetrahedra |

Convex core | Tetrakis hexahedron |

Abstract & topological properties | |

Flag count | 144 |

Schläfli type | {3,3} |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 3 |

Convex | No |

Nature | Tame |

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

This is a special case of the more general small snubahedron, with double symmetry. It can be formed from the rhombihexahedron by replacing each of the cubes with the inscribed stella octangula.

Its quotient prismatic equivalent is the tetrahedral hexateroorthowedge, which is eight-dimensional.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a small snubahedron of edge length 1 are given by all permutations of:

- .

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C5: Tets and Cubes" (#31).

- Klitzing, Richard. "snu".
- Wikipedia contributors. "Compound of six tetrahedra".