Speaker 1: Spencer Whitehead, Department of Pure Mathematics, University of Waterloo
"Regular polytopes and uniform polytopes"
A polytope is the generalization of a polyhedron to any number of dimensions. In dimensions 2 and 3, the regular polytopes are the regular polygons and the platonic solids. In higher dimensions, cubes, octahedra, and tetrahedra all still exist, and are regular. In four dimensions, there are three more exceptional regular polytopes: the 24-cell, 120-cell, and 600-cell. In 1852, Schläfli proved that this list is complete. I will present an alternate proof of Schläfli's theorem using Coxeter's theory of reflection groups. After, I will discuss extending this proof towards a classification of uniform polytopes, which are generalizations of the Archimedean solids.
Speaker 2: Brennen Young, Department of Pure Mathematics, University of Waterloo
Title and Abstract: TBA