# Square cupolic prism

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Square cupolic prism | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Squacupe |

Coxeter diagram | xx ox4xx&#x |

Elements | |

Cells | 4 triangular prisms, 1+4 cubes, 2 square cupolas, 1 octagonal prism |

Faces | 8 triangles, 2+4+4+4+8+8 squares, 2 octagons |

Edges | 4+8+8+8+8+16 |

Vertices | 8+16 |

Vertex figures | 8 isosceles trapezoidal pyramids, base edge lengths 1, √2, √2, √2, side edge length √2 |

16 irregular tetrahedra, edge lengths 1 (1), √2 (4), and √2+√2 (1) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | trip–4–cube: |

Cube–4–cube: 135º | |

Squacu–4–trip: 90° | |

Squacu–4–cube: 90° | |

Squacu–8–op: 90° | |

Trip–4–op: | |

Cube–4–op: 45° | |

Heights | Squacu atop squacu: 1 |

Cube atop op: | |

Central density | 1 |

Related polytopes | |

Army | Squacupe |

Regiment | Squacupe |

Dual | Semibisected tetragonal trapezohedral tegum |

Conjugate | Retrograde square cupolic prism |

Abstract & topological properties | |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×A_{1}×I, order 16 |

Convex | Yes |

Nature | Tame |

The **square cupolic prism**, or **squacupe**, is a CRF segmentochoron (designated K-4.69 on Richard Klitzing's list). It consiss of 2 square cupolas, 4 triangular prisms, 1+4 cubes, and 1 octagonal prism.

As the name suggests, it is a prism based on the square cupola. As such, it is a segmentochoron between two square cupolas. It can also be viewed as a segmentochoron between an octagonal prism and a cube.

Two square cupolic prisms can be attached to opposite octagonal prismatic cells of the square-octagonal duoprism to produce a small rhombicuboctahedral prism.

## Vertex coordinates[edit | edit source]

Coordinates of the vertices of a square cupolic prism of edge length 1 centered at the origin are given by:

## External links[edit | edit source]

- Klitzing, Richard. "squacupe".