# Small rhombicuboctahedral prism

The **small rhombicuboctahedral prism** or **sircope** is a prismatic uniform polychoron that consists of 2 small rhombicuboctahedra, 6+12 cubes, and 8 triangular prisms. Each vertex joins 1 small rhombicuboctahedron, 1 triangular prism, and 3 cubes. As the name suggests, it is a prism based on the small rhombicuboctahedron. As such it is also a convex segmentochoron (designated K-4.66 on Richard Klitzing's list).

Small rhombicuboctahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sircope |

Coxeter diagram | x x4o3x () |

Elements | |

Cells | 8 triangular prisms, 6+12 cubes, 2 small rhombicuboctahedra |

Faces | 16 triangles, 12+24+24+24 squares |

Edges | 24+48+48 |

Vertices | 48 |

Vertex figure | Isosceles trapezoidal pyramid, edge lengths 1, √2, √2, √2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–cube: |

Cube–4–cube: 135° | |

Sirco–4–cube: 90° | |

Sirco–3–trip: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 28 |

Level of complexity | 16 |

Related polytopes | |

Army | Sircope |

Regiment | Sircope |

Dual | Deltoidal icositetrahedral tegum |

Conjugate | Quasirhombicuboctahedral prism |

Abstract & topological properties | |

Flag count | 1536 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | B_{3}×A_{1}, order 96 |

Convex | Yes |

Nature | Tame |

The small rhombicuboctahedral prism can be obtained from the small disprismatotesseractihexadecachoron by removing 2 cube atop small rhombicuboctahedron segmentochora.

## GalleryEdit

Card with cell counts, verf, and cross-sections

Segmentochoron display, sirco atop sirco

## Vertex coordinatesEdit

The vertices of a small rhombicuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

## RepresentationsEdit

A small rhombicuboctahedral prism has the following Coxeter diagrams:

- x x4o3x (full symmetry)
- x2x4s3s ( ) (bases as snubs)
- xx4oo3xx&#x (bases considered separately)
- xxxx xxxx4oxxo&#xt (BC
_{2}×A_{1}symmetry, cube-first) - xxx wxx xwx xxw&#zx (A
_{1}×A_{1}×A_{1}×A_{1}symmetry)

## Related polychoraEdit

The small rhombicuboctahedral prism can be constructed by attaching squarre cupolic prisms to 2 opposite octagonal prisms of the square-octagonal duoprism.

The regiment of the small rhombicuboctahedral prism also includes the small cubicuboctahedral prism and the small rhombihexahedral prism.

## External linksEdit

- Bowers, Jonathan. "category 19: Prisms" (#923).

- Klitzing, Richard. "Sircope".

- Wikipedia Contributors. "Rhombicuboctahedral prism".