Spectra of semi-regular polytopes

1997/12/15 by Nicolau C. Saldanha, Carlos Tomei, Saldanha, Nicolau C. +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/9712252

arxiv created 1997/12/15 · arxiv updated 2009/11/30

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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