# Compound of two snub cubes

Compound of two snub cubes | |
---|---|

Rank | 3 |

Type | Uniform |

Notation | |

Bowers style acronym | Disco |

Coxeter diagram | ß4ß3ß () |

Elements | |

Components | 2 snub cubes |

Faces | 48 triangles, 16 triangles as 8 hexagrams, 12 squares as 6 stellated octagons |

Edges | 24+48+48 |

Vertices | 48 |

Vertex figure | Floret pentagon, edge lengths 1, 1, 1, 1, √2 |

Measures (edge length 1) | |

Circumradius | ≈ 1.34371 |

Volume | ≈ 15.77896 |

Dihedral angles | 3–3: ≈ 153.23459° |

4–3: ≈ 142.98343° | |

Central density | 2 |

Number of external pieces | 160 |

Level of complexity | 26 |

Related polytopes | |

Army | Semi-uniform Girco |

Regiment | Disco |

Dual | Compound of two pentagonal icositetrahedra |

Conjugate | Compound of two snub cubes |

Convex core | Cuboctatruncated disdyakis dodecahedron |

Abstract & topological properties | |

Flag count | 480 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}, order 48 |

Flag orbits | 10 |

Convex | No |

Nature | Tame |

The **disnub cuboctahedron**, **disco**, or **compound of two snub cubes** is a uniform polyhedron compound. It consists of 48 snub triangles, 16 further triangles, and 12 squares (the latter two can combine in pairs due to faces in the same plane). Four triangles and one square join at each vertex.

Its quotient prismatic equivalent is the snub cubic antiprism, which is four-dimensional.

## Measures[edit | edit source]

The circumradius *R* ≈ 1.34371 of the disnub cuboctahedron with unit edge length is the largest real root of

Its volume *V* ≈ 15.77896 is given by the largest real root of

- .

Its dihedral angles can be given as acos(*α*) for the angle between two triangular faces, and acos(*β*) for the angle between a square face and a triangular face, where *α* ≈ –0.89286 equals the unique real root of

and *β* ≈ –0.79846 equals the unique negative real root of

^{[1]}

## Vertex coordinates[edit | edit source]

A disnub cuboctahedron of edge length 1 has coordinates given by all permutations of:

- (±
*c*, ±_{1}*c*, ±_{2}*c*),_{3}

where

## External links[edit | edit source]

- Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#68).

- Klitzing, Richard. "disco".
- Wikipedia contributors. "Compound of two snub cubes".

- ↑ Wolfram Research, Inc. (2024). "Wolfram|Alpha Knowledgebase". Champaign, IL. "
`PolyhedronData["SnubCube", {"Circumradius", "Volume", "DihedralAngles"}]`

".