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Spectra of semi-regular polytopes

Nicolau C. Saldanha·Carlos Tomei
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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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Nicolau C. Saldanha, Carlos Tomei. 1997-12-15. Spectra of semi-regular polytopes. https://arxiv.org/abs/math/9712252

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