# Triangular-square prismantiprismoid

Triangular-square prismantiprismoid | |
---|---|

Rank | 4 |

Type | Isogonal |

Space | Spherical |

Bowers style acronym | Tispap |

Coxeter diagram | x4s2s6o () |

Elements | |

Vertex figure | Monoaugmented rectangular pyramid |

Cells | 12 wedges, 4 triangular prisms, 4 triangular antiprisms, 6 rectangular trapezoprisms |

Faces | 24 isosceles triangles, 8 triangles, 24 isosceles trapezoids, 6+12 rectangles |

Edges | 12+12+24+24 |

Vertices | 24 |

Measures (as derived from unit-edge hexagonal-octagonal duoprism) | |

Edge lengths | Short edges of rectangles (12): 1 |

Side edges (24): | |

Edges of triangles (24): | |

Long edges of rectangles (12): | |

Circumradius | |

Central density | 1 |

Euler characteristic | 0 |

Related polytopes | |

Army | Tispap |

Regiment | Tispap |

Dual | Triangular-square tegmantitegmoid |

Topological properties | |

Orientable | Yes |

Properties | |

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

Convex | Yes |

Nature | Tame |

The **triangular-square prismantiprismoid** or **tispap**, also known as the **edge-snub triangular-square duoprism** or **3-4 prismantiprismoid**, is a convex isogonal polychoron that consists of 4 triangular antiprisms, 4 triangular prisms, 6 rectangular trapezoprisms, and 12 wedges. 1 triangular antiprism, 1 triangular prism, 2 rectangular trapezoprisms, and 3 wedges join at each vertex. It can be obtained through the process of alternating one class of edges of the hexagonal-octagonal duoprism so that the octagons become rectangles. However, it cannot be made uniform, as it generally has 4 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: ≈ 1:1.57980.

## Vertex coordinates[edit | edit source]

The vertices of a triangular-square prismantiprismoid, assuming that the triangular antiprisms are regular and are connected by uniform triangular prisms of edge length 1, centered at the origin, are given by:

An alternate set of coordinates, assuming that the edge length differences are minimized, centered at the origin, are given by:

Another variant obtained from the uniform hexagonal-octagonal duoprism has coordinates given by: