# Rhombic disphenoid

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Rhombic disphenoid | |
---|---|

Rank | 3 |

Type | Noble |

Notation | |

Bowers style acronym | Rhodow |

Coxeter diagram | s2s2s () |

Elements | |

Faces | 4 scalene triangles |

Edges | 2+2+2 |

Vertices | 4 |

Vertex figure | Scalene triangle |

Measures (edge lengths a , b , c ) | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Rhodow |

Regiment | Rhodow |

Dual | Rhombic disphenoid |

Conjugate | Rhombic disphenoid |

Abstract & topological properties | |

Flag count | 24 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | K_{3}+, order 4 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

A **rhombic disphenoid** is a type of tetrahedron with 4 identical scalene triangles as faces. Rhombic disphenoids are related to tetragonal disphenoids, and can be considered to be the digonal version of gyroprisms.

A rhombic disphenoid can generally be formed by alternating a cuboid.

Rhombic disphenoids occur as cells in any n -d step prism where both n and d are even, or if n is even and d^{2} ≡ 1 mod *n* and is a divisor of 2*n*.