Wednesday, April 6th, 2016
3:00pm - 4:00pm, in McCormack 2-404

Egon Schulte

Northeastern University

Chirality in Polytopes

Abstract: A geometric structure is called chiral if it cannot be superimposed on its mirror images. We study chirality in polytopes, both abstract and geometric. Abstract polytopes are ranked combinatorial structures patterned after convex polytopes and their combinatorics. The most highly symmetric polytopes are regular or chiral. Regular polytopes have maximum reflexive combinatorial or geometric symmetry and their automorphism group or symmetry group is flag-transitive. Chiral polytopes only have maximum rotational combinatorial or geometric symmetry and their automorphism group or symmetry group has two flag-orbits represented by a pair of adjacent flags. Regular polytopes have been well-studied and much work has been done on their classification and their groups. By contrast, relatively little is known about chirality of polytopes. We describe some of the historical developments in this area and report about recent progress.