Gabe Cunningham: Abstract and Skeletal Polyhedra

Abstract and Skeletal Polyhedra

Gabe Cunningham (Wentworth Institute of Technology).

Abstract: The word "Polyhedron" has been redefined many times over the long history of geometry. In this talk, I will give an overview of two of the most recent definitions of polyhedra: abstract polyhedra, which are purely combinatorial, and skeletal polyhedra, which feature some honest geometry but are quite a bit more permissive than your great-grandfather's polyhedra. I will also briefly discuss some recent work with Daniel Pellicer, where we investigate a family of polyhedra that relaxes one of the requirements of skeletal polyhedra, giving rise to some novel and surprising behavior.