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 pi-electron energies of homo- and hetero-dodecahedron graphs have been calculated. (C) 2014 Elsevier B. V. All rights reserved.