Please note that there are several "dots with sticks"-diagrams that are used to describe polytopes, the facet-layout-diagrams being the one I myself am least acquainted with (It's best (and by my knowledge only) explanation is on this site's wiki).
The other one is the Coxeter-Dynkin-diagram, which is mainly used in Wikipedia, which is explained there but also in
this manuscript, though there I use some different notation, which I only know to be used in this forum and on Klitzings website.
Then we have something known as Dynkin-diagrams, which are used to describe root systems of "Lie-algebras", rather sophisticated mathematics that has uses in theoretical quantum physics. I know very little about that subject.