# Small biprismatorhombatodecachoron

Small biprismatorhombatodecachoron | |
---|---|

Rank | 4 |

Type | Isogonal |

Notation | |

Bowers style acronym | Sabipard |

Coxeter diagram | ac3bo3ob3ca&#zd (c < a+b/3) |

Elements | |

Cells | 20 triangular prisms, 60 wedges, 20 triangular antiprisms, 30 rectangular trapezoprisms, 10 rhombitetratetrahedra |

Faces | 40+40 triangles, 120 isosceles triangles, 60+60 rectangles, 120 isosceles trapezoids |

Edges | 60+120+120+120 |

Vertices | 120 |

Vertex figure | Triangular-rectangular wedge |

Measures (based on two prismatorhombated pentachora of edge length 1) | |

Edge lengths | Lacing edges (120): |

Remaining edges (60+120+120): 1 | |

Circumradius | |

Central density | 1 |

Related polytopes | |

Army | Sabipard |

Regiment | Sabipard |

Dual | Small bicrystallorthodecachoron |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | A_{4}×2, order 240 |

Convex | Yes |

Nature | Tame |

The **small biprismatorhombatodecachoron** or **sabipard** is a convex isogonal polychoron that consists of 10 rhombitetratetrahedra, 30 rectangular trapezoprisms, 20 triangular prisms, 20 triangular antiprisms, and 60 wedges. 1 rhombitetratetrahedron, 2 rectangular trapezoprisms, 1 triangular prism, 1 triangular antiprism, and 3 wedges join at each vertex.

It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite prismatorhombated pentachora. In this case, if the prismatorhombated pentachora are of the form a3b3o3c, then c must be less than a+b/3 (producing the transitional biprismatorhombatodecachoron in the limiting case). This includes the convex hull of two uniform prismatorhombated pentachora. The lacing edges generally have length .

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.35389.

## External links[edit | edit source]

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