Any Hückel π system with the Möbius-strip topology has a quotient property whereby its Hückel 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 Hückel and anti-Hückel monocycles, spectral embedding of twisted in untwisted cyclic polyacenes, and spectral inversion between in- and out-of-plane π sub-systems of odd-numbered rings in cluster molecules. Cartesian coordinates for Möbius graphs can be derived from those of the cylindrical parent.
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