Diffraction by regular polyhedrons

Scalar and vector problems of diffraction by regular polyhedrons (Platonic bodies)-tetrahedron, cube, octahedron, dodecahedron, and icosahedron-are co nsidered. On the basis of structural relationships of the geometric analysi s of invariant operators on regular polyhedrons and formalism of induced re presentations, the canonical forms of boundary equations are determined, wh ich are similar to the equations of the classical method of separation of v ariables in linear boundary value problems with symmetries. The results of realization of canonical forms in the scalar problem of diffraction of a pl ane wave by an octahedron with the wave dimensions ka less than or equal to 50 are presented.