Cayley graphs and symmetric 4-polytopes

Barry Monson, Asia Ivić Weiss

Abstract


Previously we have investigated the medial layer graph $\mathcal{G}$ for a finite, self-dual, regular or chiral abstract 4-polytope $\mathcal{P}$. Here we study the Cayley graph $\mathcal{C}$ on a natural group generated by polarities of $\mathcal{P}$, show that $\mathcal{C}$ covers $\mathcal{G}$ in a readily computable way and construct $\mathcal{C}$ as a voltage graph over $\mathcal{G}$. We then examine such symmetric graphs for several interesting families of polytopes of type {p,q,p}, p = 3, 4, 5.

Keywords


abstract regular or chiral polytopes, symmetric graphs

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DOI: https://doi.org/10.26493/1855-3974.79.919

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications