Tetrahedral cupolaSchlegel diagramTypePolyhedral cupolaSchläfli symbol{3,3} v rr{3,3}Cells161 rr{3,3} 1+4 {3,3} 4+6 {}×{3} Faces4224 triangles18 squaresEdges42Vertices16DualSymmetry group[3,3,1], order 24Propertiesconvex, regular-faced In 4-dimensional geometry, the tetrahedral cupola is a polychoron bounded by one tetrahedron, a parallel cuboctahedron, connected by 10 triangular prisms, and 4 triangular pyramids.Convex Segmentochora Dr. Richard Klitzing, Symmetry: Culture and Science, Vol. 11, Nos. 1-4, 139-181, 2000 (4.23 tetrahedron || cuboctahedron)
Related polytopes The tetrahedral cupola can be sliced off from a runcinated 5-cell, on a hyperplane parallel to a tetrahedral cell. The cuboctahedron base passes through the center of the runcinated 5-cell, so the Tetrahedral cupola contains half of the tetrahedron and triangular prism cells of the runcinated 5-cell. The cupola can be seen in A2 and A3 Coxeter plane orthogonal projection of the runcinated 5-cell:
A3 Coxeter planeRuncinated 5-cellTetrahedron(Cupola top)Cuboctahedron(Cupola base)A2 Coxeter plane
See also Tetrahedral pyramid (5-cell)
References
External links Segmentochora: tetaco, tet || co, K-4.23