Great rhombicosidodecahedral prism
|Great rhombicosidodecahedral prism|
|Bowers style acronym||Griddip|
|Coxeter diagram||x x5x3x ()|
|Cells||30 cubes, 20 hexagonal prisms, 12 decagonal prisms, 2 great rhombicosidodecahedra|
|Faces||60+60+60+60 squares, 40 hexagons, 24 decagons|
|Vertex figure||Irregular tetrahedron, edge lengths √2, √3, √(5+√5)/2 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of external pieces||64|
|Level of complexity||24|
|Dual||Disdyakis triacontahedral tegum|
|Conjugate||Great quasitruncated icosidodecahedral prism|
|Abstract & topological properties|
|Symmetry||H3×A1, order 240|
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).
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.
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, grid atop grid
Vertex coordinates[edit | edit source]
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:
Representations[edit | edit source]
A great rhombicosidodecahedral prism has the following Coxeter diagrams:
- x x5x3x (full symmetry)
- xx5xx3xx&#x (bases considered separately)
External links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#945).
- Klitzing, Richard. "Griddip".
- Wikipedia Contributors. "Truncated icosidodecahedral prism".