User:WolfmanSF/sandbox

List of n-dimensional mathematical problems whose solutions are most difficult or complex in four dimensions

 * Generalized Poincaré conjecture for topological manifolds (trivial for the 2-sphere, in 3 dimensions; solved in 2003 for the 3-sphere, in 4 dimensions; solved in 1982 for the 4-sphere, in 5 dimensions; solved in 1960 for n ≥ 5, in six or more dimensions
 * Convex regular polytopes (5 in three dimensions, 6 in four dimensions, 3 in all higher dimensions)
 * Regular star polytopes (4 in three dimensions, 10 in four dimensions, none in all higher dimensions)