# Rectangular trapezoprism

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Rectangular trapezoprism | |
---|---|

Rank | 3 |

Type | Isogonal |

Notation | |

Bowers style acronym | Recta |

Coxeter diagram | |

Elements | |

Faces | 4 isosceles trapezoids, 2 rectangles |

Edges | 4+4+4 |

Vertices | 8 |

Vertex figure | Scalene triangle |

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

Circumradius | |

Height | |

Central density | 1 |

Related polytopes | |

Army | Rectra |

Regiment | Rectra |

Dual | Digonal scalenohedron |

Conjugate | Rectangular trapezoprism |

Abstract & topological properties | |

Flag count | 48 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (B_{2}×A_{1})/2, order 8 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **rectangular trapezoprism** is a variant of the cube with digonal antiprism symmetry. It is isogonal, with 2 orthogonal rectangles as bases connected by 4 isosceles trapezoids. It can be obtained by bevelling two opposite edges of a tetrahedron.

If the edges of the rectangles are equal, the result is a square prism.

A version with rectangles of side lengths 1 and and lacing edges of length occurs as an edge-alternation of the uniform octagonal prism.

Specific variants of the rectangular trapezoprism can be holo-alternated to form the altered stella octangula.

## Vertex coordinates[edit | edit source]

This polytope is missing vertex coordinates. (April 2024) |

## In vertex figures[edit | edit source]

A rectangular trapezoprism with base edges of lengths 1 and and lacing edges of length occurs as the vertex figure of the antifrustary distetracontoctachoron.

## External links[edit | edit source]

- Klitzing, Richard. "rectangular trapezoprism".