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Methods for using symbolic computation systems to verify polyhedral symmetries of harmonic functions on the sphere are presented. The particular case of icosahedral symmetry, which is important in the structure of small spherical viruses, fullerenes, and quasi-crystals, is examined in detail. Previous work by the authors, in which general expressions for polyhedral harmonics in terms of spherical harmonics were derived, is verified by checking the symmetry of all icosahedral harmonics up to order 44.
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