  A family of maximally superintegrable systems containing the Coulomb atom as
a special case is constructed in N-dimensional Euclidean space. Two different
sets of N commuting second order operators are found, overlapping in the
Hamiltonian alone. The system is separable in several coordinate systems and is
shown to be exactly solvable. It is solved in terms of classical orthogonal
polynomials. The Hamiltonian and N further operators are shown to lie in the
enveloping algebra of a hidden affine Lie algebra.
