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|
|Bowers style acronym||Sircope|
|Coxeter diagram||x x4o3x ()|
|Cells||8 triangular prisms, 6+12 cubes, 2 small rhombicuboctahedra|
|Faces||16 triangles, 12+24+24+24 squares|
|Vertex figure||Isosceles trapezoidal pyramid, edge lengths 1, √2, √2, √2 (base), √2 (legs)|
|Measures (edge length 1)|
|Number of external pieces||28|
|Level of complexity||16|
|Dual||Deltoidal icositetrahedral tegum|
|Abstract & topological properties|
|Symmetry||B3×A1, order 96|
The small rhombicuboctahedral prism can be obtained from the small disprismatotesseractihexadecachoron by removing 2 cube atop small rhombicuboctahedron segmentochora.
Card with cell counts, verf, and cross-sections
Segmentochoron display, sirco atop sirco
The vertices of a small rhombicuboctahedral prism of edge length 1 are given by all permutations of the first three coordinates of:
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 (BC2×A1 symmetry, cube-first)
- xxx wxx xwx xxw&#zx (A1×A1×A1×A1 symmetry)
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.
- Bowers, Jonathan. "category 19: Prisms" (#923).
- Klitzing, Richard. "Sircope".
- Wikipedia Contributors. "Rhombicuboctahedral prism".