abstract: Given a Gelfand pair (G,K) formed by the action of a compact group K on the Heisenberg group, we construct a new topological model for the Gelfand space. Each point in the Gelfand space is associated with a particular K-orbit in the dual of the Lie algebra of the Heisenberg group. We construct a set of "eigenvalue polynomials" which define the K-orbits.