Some explicit results for three-dimensional Helmholtz operator in polyhedra

The paper develops a new method for three-dimensional Helmholtz operator in closed spaces which involves some new solutions for polyhedral shapes in explicit form. The method is based on the technique of virtual sources. It is shown that exact solutions can be constructed for those polyhedron geometries, where all interior dihedral angels are π/n (n is an integer). Some new explicit formulae are obtained for eigenfrequencies of the triangular prisms.