Octahedral cupolaSchlegel diagramTypePolyhedral cupolaSchläfli symbol{3,4} v rr{3,4}Cells281 {3,4} 1 rr{4,3} 8+12 {}×{3} 6 {}v{4} Faces8240 triangles42 squaresEdges84Vertices30DualSymmetry group[4,3,1], order 48Propertiesconvex, regular-faced In 4-dimensional geometry, the octahedral cupola is a 4-polytope bounded by one octahedron and a parallel rhombicuboctahedron, connected by 20 triangular prisms, and 6 square pyramids.Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.107 octahedron || rhombicuboctahedron)
Related polytopes The octahedral cupola can be sliced off from a runcinated 24-cell, on a hyperplane parallel to an octahedral cell. The cupola can be seen in a B2 and B3 Coxeter plane orthogonal projection of the runcinated 24-cell: Runcinated 24-cellOctahedron(cupola top)Rhombicuboctahedron(cupola base)B3 Coxeter planeB2 Coxeter plane
See also Octahedral pyramid Cubic cupola Runcinated 24-cell
References
External links Segmentochora: oct || sirco, K-4.107