Graduate Student Seminar (GSS) Talk

October 27, 2021 - 3:00 PM to 3:45 PM
Fretwell 315
Title: Generating simplicial complexes for higher dimensional polytopes
Speaker: Jacob Raymond
Description: The symmetry groups of certain polytopes are isomorphic to the class of reflection groups known as Coxeter groups. Using the Todd-Coxeter coset enumeration algorithm, and a representation of the group as a group of Householder linear reflections, the vertices of the original polytope can be recovered. I present an algorithm to recover the edges, faces, volumes, and higher dimensional volumes in addition to the vertices, forming a simplicial complex corresponding to the polytope. This information can then be used to generate interesting and insightful visualizations of higher dimensional objects.