Small rhombicosidodecahedral prism
|Small rhombicosidodecahedral prism|
|Bowers style acronym||Sriddip|
|Coxeter diagram||x x5o3x ()|
|Cells||20 triangular prisms, 30 cubes, 12 pentagonal prisms, 2 small rhombicosidodecahedra|
|Faces||40 triangles, 60+60+60 squares, 24 pentagons|
|Vertex figure||Isosceles trapezoidal pyramid, edge lengths 1, √2, (1+√5)/2, √2 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of external pieces||64|
|Level of complexity||16|
|Dual||Deltoidal hexecontahedral tegum|
|Abstract & topological properties|
|Symmetry||H3×A1, order 240|
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).
The small rhombicosidodecahedral prism can be vertex-inscribed into the small ditetrahedronary hexacosihecatonicosachoron.
Gallery[edit | edit source]
Card with cell counts, verf, and cross-sections
Segmentochoron display, srid atop srid
Vertex coordinates[edit | edit source]
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:
Representations[edit | edit source]
The small rhombicosidodecahedral prism has the following Coxeter diagrams:
- x x5o3x (full symmetry)
- xx5oo3xx&#x (bases considered separately)
Related polychora[edit | edit source]
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 links[edit | edit source]
- Bowers, Jonathan. "Category 19: Prisms" (#926).
- Klitzing, Richard. "Sriddip".
- Wikipedia Contributors. "Rhombicosidodecahedral prism".