Huckel spectra of Mobius π systems

Any Huckel pi system with the Mobius-strip topology has a quotient property whereby its Huckel spectrum is the ungerade, and its adjacency spectrum the gerade half of the spectrum of a centrosymmetric cylindrical graph with twice as many vertices. Consequences include the spectral complementarity of Huckel and anti-Huckel monocycles, spectral embedding of twisted in untwisted cyclic polyacenes, and spectral inversion between in- and out-of-plane pi sub-systems of odd-numbered rings in cluster molecules. Cartesian coordinates for Mobius graphs can be derived from those of the cylindrical parent.