# Square-hexagonal duoprism

Jump to navigation
Jump to search

Square-hexagonal duoprism | |
---|---|

Rank | 4 |

Type | Uniform |

Notation | |

Bowers style acronym | Shiddip |

Coxeter diagram | x4o x6o () |

Elements | |

Cells | 6 cubes, 4 hexagonal prisms |

Faces | 6+24 squares, 4 hexagons |

Edges | 24+24 |

Vertices | 24 |

Vertex figure | Digonal disphenoid, edge lengths √3 (base 1) and √2 (base 2 and sides) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–cube: 120° |

Cube–4–hip: 90° | |

Hip–4–hip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 10 |

Level of complexity | 6 |

Related polytopes | |

Army | Shiddip |

Regiment | Shiddip |

Dual | Square-hexagonal duotegum |

Conjugate | None |

Abstract & topological properties | |

Flag count | 576 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{2}×G_{2}, order 96 |

Flag orbits | 6 |

Convex | Yes |

Nature | Tame |

The **square-hexagonal duoprism** or **shiddip**, also known as the **4-6 duoprism**, is a uniform duoprism that consists of 4 hexagonal prisms and 6 cubes, with two of each joining at each vertex.s.

It is also a CRF segmentochoron, being hexagonal prism atop hexagonal prism. It is designated K-4.54 on Richard Klitzing's list. As It can thus be thought of as a prism based on the hexagonal prism.

This polychoron can be alternated into a digonal-triangular duoantiprism, although it cannot be made uniform.

## Gallery[edit | edit source]

## Vertex coordinates[edit | edit source]

The vertices of a square-hexagonal duoprism of edge length 1, centered at the origin, are given by:

- ,
- .

## Representations[edit | edit source]

A square-hexagonal duoprism has the following Coxeter diagrams:

- x4o x6o () (full symmetry)
- x x x6o () (G
_{2}×K_{2}symmetry, square as rectangle) - x3x x4o () (A
_{2}×B_{2}symmetry, hexagon as ditrigon) - x x x3x () (A
_{2}×K_{2}symmetry, both above combined - xx xx6oo&#x (G
_{2}×A_{1}axial, hexagonal prism prism) - xx xx3xx&#x (A
_{2}×A_{1}symmetry, as above with ditrigon symmetry) - xux xxx4ooo&#xt (B
_{2}×A_{1}axial, cube-first) - xux xxx xxx&#xt (K
_{3}axial, cube-first) - oqo xxx6ooo&#xt (G
_{2}×A_{1}axial, hexagon-first) - oqo xxx3xxx&#xt (A
_{2}×A_{1}axial, hexagon-first)

## External links[edit | edit source]

- Bowers, Jonathan. "Category A: duoprisms".

- Klitzing, Richard. "shiddip".
- Wikipedia contributors. "4-6 duoprism".