Wednesday, April 18th, 2018
12:00 pm - 1:00 pm, in Science 2-063

Daniel Pellicier

UNAM (Mexico)

Chiral 4-polytopes in Euclidean space

Abstract: By a polyhedron we understand a connected structure consisting of vertices (points in space), edges (line segments) and polygons, where every edge belongs to two polygons. We do not assume that the polygons are convex, planar or even finite. A 4-polytope is a connected collection of polyhedra where every polygon belongs to two polyhedra. A 4-polytope is regular whenever every local combinatorial reflection can be extended to an isometry of space preserving the polytope. If this is possible for every local combinatorial rotation, but not for the reflections we say that the 4-polytope is chiral. In 2004 Peter McMullen claimed that there are no chiral 4-polytopes in Euclidean space. This result turned out to be false. In this talk we describe the three chiral 4-polytopes in Euclidean space