# Disdyakis dodecahedron

Disdyakis dodecahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Siddykid |

Coxeter diagram | m4m3m () |

Conway notation | mC |

Elements | |

Faces | 48 scalene triangles |

Edges | 24+24+24 |

Vertices | 6+8+12 |

Vertex figure | 6 octagons, 8 hexagons, 12 squares |

Measures | |

Dihedral angle | |

Central density | 1 |

Number of external pieces | 48 |

Level of complexity | 6 |

Related polytopes | |

Army | Siddykid |

Regiment | Siddykid |

Dual | Great rhombicuboctahedron |

Conjugate | Great disdyakis dodecahedron |

Abstract & topological properties | |

Flag count | 288 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | Yes |

Nature | Tame |

The **disdyakis dodecahedron**, also called the **small disdyakis dodecahedron**, is one of the 13 Catalan solids. It has 48 scalene triangles as faces, with 6 order-8, 8 order-6, and 12 order-4 vertices. It is the dual of the uniform great rhombicuboctahedron.

It can also be obtained as the convex hull of a cube, an octahedron, and a cuboctahedron. If the cube has unit edge length, the octahedron's edge length is and the cuboctahedron's edge length is .

Each face of this polyhedron is a scalene triangle. If the shortest edges have unit edge length, the medium edges have length and the longest edges have length . These triangles have angles measuring , , and .

## Vertex coordinates[edit | edit source]

A disdyakis dodecahedron with dual edge length 1 has vertex coordinates given by all permutations of:

## External links[edit | edit source]

- Klitzing, Richard. "Siddykid".
- Wikipedia contributors. "Disdyakis dodecahedron".
- McCooey, David. "Disdyakis Dodecahedron"

- Quickfur. "The Disdyakis Dodecahedron".