  A class of two-dimensional superintegrable systems on a constant curvature
surface is considered as the natural generalization of some well known
one-dimensional factorized systems. By using standard methods to find the
shape-invariant intertwining operators we arrive at a $so(6)$ dynamical algebra
and its Hamiltonian hierarchies. We pay attention to those associated to
certain unitary irreducible representations that can be displayed by means of
three-dimensional polyhedral lattices. We also discuss the role of
superpotentials in this new context.
