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 ?$\{p,q,p\}$?, ?$p = 3,4,5$?.

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URN

URN:NBN:SI:doc-GR1OQVXL

COBISSID

15152729

Added

16.12.2021

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Citation

APA:

Monson, Barry, Ivić Weiss, Asia (2008). Cayley graphs and symmetric 4-polytopes. Ars mathematica contemporanea, volume 1, issue 2, str. 185-205. URN:NBN:SI:doc-GR1OQVXL from http://www.dlib.si

MLA:

Monson, Barry, Ivić Weiss, Asia. "Cayley graphs and symmetric 4-polytopes." Ars mathematica contemporanea volume 1. issue 2 (2008) str. 185-205.
<http://www.dlib.si/?URN=URN:NBN:SI:doc-GR1OQVXL>

Ars mathematica contemporanea
2008-
(Assembly record)