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Polytopal Digraphs and the Gale transform
Student-Run Research Seminar| Speaker: | Jed Mihalisin, Dept. of Mathematics UC Berkeley |
| Location: | 593 Kerr |
| Start time: | Thu, Oct 18 2001, 10:00AM |
Analogous to the definition of a graph as {\em $d$-polytopal} if it is isomorphic to the edge graph of a $d$ dimensional polytope, a directed graph is defined to be {\em $d$-polytopal} if its underlying graph is $d$-polytopal and its orientation may be induced by a linear functional acting on the polytope. This talk will demonstrate the utility of the Gale Transform in exploring the characterization of polytopal digraphs. The examples of few vertex polytopes and Lawrence polytopes will illustrate the direct utility of the Gale transform. The examples of few facet polytopes as well as the $4$-cube will illustrate the utility of the Gale transform as applied to the dual of a polytope.