Eigensolutions of dodecahedron graphs

Eigensolutions of 20-vertex cage (i.e. dodecahedron) have been determined with the use of fivefold rotational symmetry. For homo-dodecahedron the eigensolutions become analytical but for the hetero-dodecahedron having two different types of atoms ( ( C , N ) , ( C , B ) , ( B , N ) ) the eigensolutions are found to be factored out into five 4-degree polynomials with one corresponding to nondegenerate and other four corresponding to two degenerate eigensolutions. Eigenspectra and total π-electron energies of homo- and hetero-dodecahedron graphs have been calculated.