# Digonal-triangular duoantiprism

Digonal-triangular duoantiprism | |
---|---|

File:Digonal-triangular duoantiprism.png | |

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Notation | |

Bowers style acronym | Ditdap |

Coxeter diagram | s4o2s6o () |

Elements | |

Cells | 12 digonal disphenoids, 6 tetragonal disphenoids, 4 triangular antiprisms |

Faces | 24+24 isosceles triangles, 4 triangles |

Edges | 6+12+24 |

Vertices | 12 |

Vertex figure | Augmented triangular prism |

Measures (based on component polygons of edge length 1) | |

Edge lengths | Lacing edges (24): |

Digons (6): 1 | |

Edges of triangles (12): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Ditdap |

Regiment | Ditdap |

Dual | Digonal-triangular duoantitegum |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | (B_{2}×G_{2})/2, order 48 |

Convex | Yes |

Nature | Tame |

The **digonal-triangular duoantiprism** or **ditdap**, also known as the **2-3 duoantiprism**, is a convex isogonal polychoron that consists of 4 triangular antiprisms, 6 tetragonal disphenoids, and 12 digonal disphenoids. 2 triangular antiprisms, 2 tetragonal disphenoids, and 4 digonal disphenoids join at each vertex. It can be obtained through the process of alternating the square-hexagonal duoprism. However, it cannot be made uniform, as it generally has 3 edge lengths, which can be minimized to no fewer than 2 different sizes.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.09545. In this specific variant the digonal disphenoids become tetragonal disphenoids. A variant where the triangular antiprisms become fully regular octahedra also exists.

## Vertex coordinates[edit | edit source]

The vertices of a digonal-triangular duoantiprism, assuming that the triangular antiprisms are regular octahedra of edge length 1, centered at the origin, are given by:

with all even changes of sign, and

with all odd changes of sign except for the first coordinate.

An alternate set of coordinates where the digonal disphenoids become tetragonal disphenoids, centered at the origin, are given by:

with all even changes of sign, and

with all odd changes of sign except for the first coordinate.

## External links[edit | edit source]

- Klitzing, Richard. "ditdap".