A polyhedron of genus $p$ is harmonic if the number of its faces (vertices) is the harmonic mean of its numbers of its edges and vertices (faces). The determination of all permissible combinations of numbers of vertices, edges, and faces is reduced to solution of Pen’s equation.
Realizations of all such polyhedra with $p = 1$ are described, as well as for all negative p with large enough numbers of edges.
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