# Square antitegum

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Square antitegum | |
---|---|

Rank | 3 |

Type | Uniform dual |

Notation | |

Bowers style acronym | Squate |

Coxeter diagram | p2p8o () |

Conway notation | dA4 |

Elements | |

Faces | 8 kites |

Edges | 8+8 |

Vertices | 2+8 |

Vertex figure | 8 triangles, 2 squares |

Measures (edge length 1) | |

Dihedral angle | |

Central density | 1 |

Number of external pieces | 8 |

Level of complexity | 4 |

Related polytopes | |

Army | Squate |

Regiment | Squate |

Dual | Square antiprism |

Conjugate | Square antitegum |

Abstract & topological properties | |

Flag count | 64 |

Euler characteristic | 2 |

Surface | Sphere |

Orientable | Yes |

Genus | 0 |

Properties | |

Symmetry | (I_{2}(8)×A_{1})/2, order 16 |

Convex | Yes |

Nature | Tame |

The **square antitegum**, also known as the **tetragonal trapezohedron**, is an antitegum based on the square, constructed as the dual of a square antiprism. It has 8 kites as faces, with 2 order–4 and 8 order–3 vertices.

Each face of this polyhedron is a kite with its longer edges times the length of its shorter edges.

The square antitegum (with theoretical edge length 1) is the vertex figure of the triangular-gyroprismatic enneacontahexachoron, which cannot be made uniform.

## External links[edit | edit source]

- Wikipedia contributors. "Tetragonal trapezohedron".
- McCooey, David. "Tetragonal Trapezohedron"
- Quickfur. "The Square Trapezohedron".