# Square scalene

Square scalene | |
---|---|

Rank | 4 |

Type | Segmentotope |

Notation | |

Bowers style acronym | Squasc |

Coxeter diagram | xo ox4oo&#x |

Tapertopic notation | [11]^{2} |

Elements | |

Cells | |

Faces | |

Edges | 1+4+8 |

Vertices | 2+4 |

Vertex figures | 2 square pyramids, edge length 1 |

4 digonal disphenoids, edge lengths √2 (1 base) and 1 (remaining edges) | |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Tet–3–tet: 120° |

Squippy–4–squippy: 90° | |

Tet–3–squippy: 60° | |

Heights | Point atop squippy: |

Dyad atop tet: | |

Trig atop inclined trig: | |

Dyad atop perp square: | |

Central density | 1 |

Related polytopes | |

Army | Squasc |

Regiment | Squasc |

Dual | Square scalene |

Conjugate | None |

Abstract & topological properties | |

Flag count | 160 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×A_{1}×I, order 16 |

Flag orbits | 10 |

Convex | Yes |

Nature | Tame |

The **square scalene** (OBSA: **squasc**), or **square pyramidal pyramid**, is a CRF segmentochoron (designated K-4.4 on Richard Klitzing's list). It consists of 2 square pyramids and 4 tetrahedra. It can be thought of as a pyramid based on the square pyramid.

Apart from being a point atop square pyramid, it has alternate segmentochoron representations as a dyad atop tetrahedron, dyad atop perpendicular square and triangle atop inclined triangle.

It can be viewed as a quarter of the hexadecachoron or a half of the octahedral pyramid.

## Vertex coordinates[edit | edit source]

The vertices of a square scalene with unit edge length are given by:

- ,
- ,
- ,
- .

It can also be given by the integral coordinates:

- ,
- .

## Representations[edit | edit source]

The square scalene has the following Coxeter diagrams:

- xo ox4oo&#x (full symmetry, dyad atop fully orthogonal square)
- xo ox ox&#x (A1×A1×A1 symmetry, rectangle scalene)
- oox4ooo&#x (BC2 symmetry, square pyramidal pyramid)
- oox oox&#x (A1×A1 symmetry, rectangle pyramid pyramid)
- xoo oxx&#x (A1×A1 symmetry, trapezoid scalene)
- xoox&#x (bilateral symmetry only)

## External links[edit | edit source]

- Klitzing, Richard. "squasc".
- Wikipedia contributors. "Square-pyramidal pyramid".