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Polytopal Digraphs and the Gale transform
Student-Run Research| Speaker: | Jed Mihalisin, Dept. of Mathematics UC Berkeley |
| Location: | 593 Kerr |
| Start time: | Thu, Oct 18 2001, 10:00AM |
Description
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.