# Deltoidal icositetrahedron

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Deltoidal icositetrahedron | |
---|---|

Rank | 3 |

Type | Uniform dual |

Space | Spherical |

Notation | |

Bowers style acronym | Sladid |

Coxeter diagram | m4o3m |

Elements | |

Faces | 24 kites |

Edges | 24+24 |

Vertices | 6+8+12 |

Vertex figure | 8 triangles, 6+12 squares |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Related polytopes | |

Army | Sladid |

Regiment | Sladid |

Dual | Small rhombicuboctahedron |

Conjugate | Great deltoidal icositetrahedron |

Abstract properties | |

Euler characteristic | 2 |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{3}, order 48 |

Convex | Yes |

Nature | Tame |

The **deltoidal icositetrahedron**, also called the **strombic icositetrahedron** or **small lanceal disdodecahedron**, is one of the 13 Catalan solids. It has 24 kites as faces, with 6+12 order-4 and 8 order-3 vertices. It is the dual of the uniform small 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 kite with its longer edges times the length of its shorter edges. These kites have three angles measuring and one angle measuring .

## Vertex coordinates[edit | edit source]

A deltoidal icositetrahedron with dual edge length 1 has vertex coordinates given by all permutations of:

## External links[edit | edit source]

- Klitzing, Richard. "Sladid".

- Wikipedia Contributors. "Deltoidal icositetrahedron".
- McCooey, David. "Deltoidal Icositetrahedron"