# Small rhombicosidodecahedral prism

The **small rhombicosidodecahedral prism** or **sriddip** is a prismatic uniform polychoron that consists of 2 small rhombicosidodecahedra, 12 pentagonal prisms, 20 triangular prisms, and 30 cubes. Each vertex joins 1 small rhombicosidodecahedron, 1 pentagonal prism, 1 triangular prism, and 2 cubes. As the name suggests, it is a prism based on the small rhombicosidodecahedron. As such it is also a convex segmentochoron (designated K-4.111 on Richard Klitzing's list).

Small rhombicosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Sriddip |

Coxeter diagram | x x5o3x () |

Elements | |

Cells | 20 triangular prisms, 30 cubes, 12 pentagonal prisms, 2 small rhombicosidodecahedra |

Faces | 40 triangles, 60+60+60 squares, 24 pentagons |

Edges | 60+120+120 |

Vertices | 120 |

Vertex figure | Isosceles trapezoidal pyramid, edge lengths 1, √2, (1+√5)/2, √2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Trip–4–cube: |

Cube–4–pip: | |

Srid–5–pip: 90° | |

Srid–3–trip: 90° | |

Srid–4–cube: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 64 |

Level of complexity | 16 |

Related polytopes | |

Army | Sriddip |

Regiment | Sriddip |

Dual | Deltoidal hexecontahedral tegum |

Conjugate | Quasirhombicosidodecahedral prism |

Abstract & topological properties | |

Flag count | 3840 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | Yes |

Nature | Tame |

The small rhombicosidodecahedral prism can be vertex-inscribed into the small ditetrahedronary hexacosihecatonicosachoron.

## GalleryEdit

Card with cell counts, verf, and cross-sections

Segmentochoron display, srid atop srid

## Vertex coordinatesEdit

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

along with all even permutations of the first three coordinates of:

## RepresentationsEdit

The small rhombicosidodecahedral prism has the following Coxeter diagrams:

- x x5o3x (full symmetry)
- xx5oo3xx&#x (bases considered separately)

## Related polychoraEdit

The pentagonal cupolic prism is a segmentochoron that can be obtained as a cap of the small rhombicosidodecahedral prism.

The regiment of the small rhombicosidodecahedral prism also includes the small dodecicosidodecahedral prism and the small rhombidodecahedral prism.

## External linksEdit

- Bowers, Jonathan. "Category 19: Prisms" (#926).

- Klitzing, Richard. "Sriddip".

- Wikipedia Contributors. "Rhombicosidodecahedral prism".