Abstract
We compute the spectra of the adjacency matrices of the semi-regular polytopes. A few different techniques are employed: the most sophisticated, which relates the 1-skeleton of the polytope to a Cayley graph, is based on methods akin to those of Lovász and Babai ([L], [B]). It turns out that the algebraic degree of the eigenvalues is at most 5, achieved at two 3-dimensional solids.
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Dedicated to the memory of R. Mañé
Research supported by MCT and CNPq, Brazil.
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Saldanha, N.C., Tomei, C. Spectra of semi-regular polytopes. Bol. Soc. Bras. Mat 29, 25–51 (1998). https://doi.org/10.1007/BF01245867
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DOI: https://doi.org/10.1007/BF01245867