Algebra Associated with the Hasse Graphs of Polytopes

Abstract

There is a Hasse graph associated with each symmetry of every n-dimensional polytope, and there is an algebra associated with each Hasse graph. Our goal is to determine the structure of all of the algebras associated with finite Coxeter groups (consisting of 4 families and 6 exceptional groups) by determining all Hasse graph polynomials f(t). Duffy and past student research groups have accomplished finding the Hasse graph polynomials for the algebras associated with the An; Bn; Dn; I2(p) families and H3. We are working on the 600-Cell (H4). Methodology