  Kepler (1619) and Croft (1980) have considered largest homothetic copies of
one regular polytope contained in another regular polytope. For arbitrary pairs
of polytopes we propose to model this as a quadratically constrained
optimization problem. These problems can then be solved numerically; in case
the optimal solutions are algebraic, exact optima can be recovered by solving
systems of equations to very high precision and then using integer relation
algorithms. Based on this approach, we complete Croft's solution to the problem
concerning maximal inclusions of regular three-dimensional polyhedra by
describing inclusions for the six remaining cases.
