# Square prism

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

Rank | 3 |

Type | Semi-uniform |

Notation | |

Bowers style acronym | Squip |

Coxeter diagram | x y4o |

Elements | |

Faces | 4 rectangles, 2 squares |

Edges | 4+8 |

Vertices | 8 |

Vertex figure | Isosceles triangle |

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

Circumradius | |

Volume | |

Dihedral angle | 90° |

Height | |

Central density | 1 |

Related polytopes | |

Army | Squip |

Regiment | Squip |

Dual | Square tegum |

Conjugate | Square prism |

Abstract & topological properties | |

Flag count | 48 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | B_{2}×A_{1}, order 16 |

Flag orbits | 3 |

Convex | Yes |

Nature | Tame |

The **square prism**, or **squip**, is a prism with a square base. The uniform square prism is simply the regular cube. If the edges of the base square and the side edges of the prism are different, the result is a semi-uniform polyhedron with 2 squares and 4 rectangles as faces.

A square prism with base edges of length a and side edges of length b can be alternated into a tetragonal disphenoid with base edges of length and side edges of length .

## Vertex coordinates[edit | edit source]

A square prism with base edges of length a and side edges of length b has coordinates given by:

- .

## In vertex figures[edit | edit source]

A square prism with base edges of length 1 and side edges of length occurs as the vertex figure of the Euclidean rectified cubic honeycomb.