Twenty irregular tetrahedra pack with a common vertex in such a way that the twelve outer vertices form a regular icosahedron. Indeed, the icosahedron edge length l is slightly longer than the circumsphere radius r (l ≈ 1.05 r). There is a solution with regular tetrahedra if the space is not Euclidean, but spherical. It is the polytope {3,3,5}, using the Schläfli notation, also known as the 600-cell.