# Tetragonal disphenoid

Tetragonal disphenoid | |
---|---|

Rank | 3 |

Type | Noble |

Space | Spherical |

Bowers style acronym | Tedow |

Coxeter diagram | xo ox&#y |

Elements | |

Vertex figure | Isosceles triangle |

Faces | 4 isosceles triangles |

Edges | 2+4 |

Vertices | 4 |

Measures (edge lengths b [base], ℓ [lacing]) | |

Circumradius | |

Height | |

Central density | 1 |

Euler characteristic | 2 |

Related polytopes | |

Army | Tedow |

Dual | Tetragonal disphenoid |

Topological properties | |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (B_{2}×A_{1})/2, order 8 |

Convex | Yes |

Nature | Tame |

The **tetragonal disphenoid** or **tedow** is a type of tetrahedron with four identical isosceles triangles for faces. It can also be considered a digonal antiprism. Tetragonal disphenoids, being digonal antiprisms, are related to rhombic disphenoids, which are digonal gyroprisms.

The general tetragonal disphenoid can be obtained as the alternation of a square prism. If the tetragonal disphenoid's base edges are of length b and its side edges are of length l, the corresponding square prism has base edge length and side edge length .

## Vertex coordinates[edit | edit source]

The vertices of a tetragonal disphenoid with base edges of length b and side edges of length l are given by all even sign changes of:

## In vertex figures[edit | edit source]

Tetragonal disphenoids occur as vertex figures in 3 noble uniform polychora: the decachoron, the tetracontoctachoron, and the great tetracontoctachoron. They also appear as the vertex figure of any duoprism of two identical polygons.