# Great rhombicosidodecahedral prism

The **great rhombicosidodecahedral prism** or **griddip** is a prismatic uniform polychoron that consists of 2 great rhombicosidodecahedra, 12 decagonal prisms, 20 hexagonal prisms, and 30 cubes. Each vertex joins one of each type of cell. It is a prism based on the great rhombicosidodecahedron. As such it is also a convex segmentochoron (designated K-4.150 on Richard Klitzing's list).

Great rhombicosidodecahedral prism | |
---|---|

Rank | 4 |

Type | Uniform |

Space | Spherical |

Notation | |

Bowers style acronym | Griddip |

Coxeter diagram | x x5x3x () |

Elements | |

Cells | 30 cubes, 20 hexagonal prisms, 12 decagonal prisms, 2 great rhombicosidodecahedra |

Faces | 60+60+60+60 squares, 40 hexagons, 24 decagons |

Edges | 120+120+120+120 |

Vertices | 240 |

Vertex figure | Irregular tetrahedron, edge lengths √2, √3, √(5+√5)/2 (base), √2 (legs) |

Measures (edge length 1) | |

Circumradius | |

Hypervolume | |

Dichoral angles | Cube–4–hip: |

Cube–4–dip: | |

Hip–4–dip: | |

Grid–10–dip: 90° | |

Grid–6–hip: 90° | |

Grid–4–cube: 90° | |

Height | 1 |

Central density | 1 |

Number of external pieces | 64 |

Level of complexity | 24 |

Related polytopes | |

Army | Griddip |

Regiment | Griddip |

Dual | Disdyakis triacontahedral tegum |

Conjugate | Great quasitruncated icosidodecahedral prism |

Abstract & topological properties | |

Flag count | 5760 |

Euler characteristic | 0 |

Orientable | Yes |

Properties | |

Symmetry | H_{3}×A_{1}, order 240 |

Convex | Yes |

Nature | Tame |

This polychoron can be alternated into a snub dodecahedral antiprism, which cannot be made uniform.

The great rhombicosidodecahedral pirsm can be vertex-inscribed into the small tritrigonary prismatohecatonicosidishexacosichoron.

## GalleryEdit

Card with cell counts, verf, and cross-sections

Segmentochoron display, grid atop grid

## Vertex coordinatesEdit

The vertices of a great 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

A great rhombicosidodecahedral prism has the following Coxeter diagrams:

- x x5x3x (full symmetry)
- xx5xx3xx&#x (bases considered separately)

## External linksEdit

- Bowers, Jonathan. "Category 19: Prisms" (#945).

- Klitzing, Richard. "Griddip".

- Wikipedia Contributors. "Truncated icosidodecahedral prism".