# Rectified small prismatodecachoron

Rectified small prismatodecachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Respid |

Coxeter diagram | uo3ox3xo3ou&#zq |

Elements | |

Cells | 20 triangular antiprisms, 10 octahedra, 20 rectified triangular prisms |

Faces | 120 isosceles triangles, 40+40 triangles, 300 squares |

Edges | 120+120 |

Vertices | 60 |

Vertex figure | Isosceles trapezoidal prism |

Measures (short edge length 1) | |

Edge lengths | Edges of triangles (120): 1 |

Lacing edges (120): | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Respid |

Regiment | Respid |

Dual | Joined triangular-antitegmatic icosachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}×2, order 240 |

Convex | Yes |

Nature | Tame |

The **rectified small prismatodecachoron** or **respid** is a convex isogonal polychoron that consists of 10 octahedra, 20 rectified triangular prisms, and 20 triangular antiprisms. 1 octahedron, 3 rectified triangular prisms, and 2 triangular antiprisms join at each vertex. It can be formed by rectifying the small prismatodecachoron.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the small rhombated pentachoron, where the edges of the octahedra are half the length of the other edges. It is one of five polychora (including two transitional cases) formed from two small rhombated pentachora, and is the transitional point between the small birhombatodecachoron and medial birhombatodecachoron.

The ratio between the longest and shortest edges is 1: ≈ 1:1.41421.

## External links[edit | edit source]

- Bowers, Jonathan. "Pennic and Decaic Isogonals".

- Klitzing, Richard. "respid".