Rhombicuboctahedral prismTypePrismatic uniform polychoronUniform index53Schläfli symbolt0,2,3{3,4,2} or rr{3,4}×{}s2,3{3,4,2} or s2{3,4}×{}Coxeter diagramCells28 total:2 rr{4,3} or s2{3,4}8 {}x{3}18 {4,3}Faces100 total:16 {3}84 {4}Edges120Vertices48Vertex figureTrapezoidal pyramidSymmetry group[4,3,2], order 96[3+,4,2], order 48Propertiesconvex In geometry, a rhombicuboctahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Images NetSchlegel diagramOne rhombicuboctahedron and triangular prisms show
Alternative names small rhombicuboctahedral prism (Small) rhombicuboctahedral dyadic prism (Norman W. Johnson) Sircope (Jonathan Bowers: for small-rhombicuboctahedral prism) (small) rhombicuboctahedral hyperprism
Related polytopes Runcic snub cubic hosochoron Runcic snub cubic hosochoronSchläfli symbols3{2,4,3}Coxeter diagramCells16 total: 2 t{3,3} 6 {3,3} 8 tricup Faces52 total:32 {3}12{4}8 {6}Edges60Vertices 24Vertex figureSymmetry group[4,3,2+], order 48Propertiesconvex A related polychoron is the runcic snub cubic hosochoron, also known as a parabidiminished rectified tesseract, truncated tetrahedral alterprism, or truncated tetrahedral cupoliprism, s3{2,4,3}, . It is made from 2 truncated tetrahedra, 6 tetrahedra, and 8 triangular cupolae in the gaps, for a total of 16 cells, 52 faces, 60 edges, and 24 vertices. It is vertex-transitive, and equilateral, but not uniform, due to the cupolae. It has symmetry [2+,4,3], order 48.Category S1: Simple Scaliforms Tutcuphttp://bendwavy.org/klitzing/pdf/artConvSeg_8.pdf 4.55 truncated tetrahedron || inverse truncated tetrahedron
It is related to the 16-cell in its s{2,4,3}, construction.
It can also be seen as a prismatic polytope with two parallel truncated tetrahedra in dual positions, as seen in the compound of two truncated tetrahedra. Triangular cupolae connect the triangular and hexagonal faces, and the tetrahedral connect edge-wise between. Projection(triangular cupolae hidden)Net
References
External links