Abstract: Packings and tilings of shapes have been of interest to mathematicians, physicists, and puzzlers for millenia. Certain shapes can pack densely to tile space in 2D or 3D. Others cannot tile space, and thus the arrangements that allow them to pack most densely (but with packing fraction necessarily less than one) are of interest for fundamental as well as practical reasons. At lower packing fractions than those that produce densest packings, statistical thermodynamics permits the ordering of many shapes into periodic and aperiodic structures by self-assembly. For some shapes, these ordered assemblies are structurally identical to the shape's (putative) densest packing, but more interesting, and possibly more common, is when the assemblies and densest packings are different. Here we discuss the packing, tiling and self-assembly of polyhedra and polygons, including the curious case of the tetrahedron, where the simplest 3D shape assembles into one of the most complex ordered structures - a quasicrystal.

Event will take place in-person in 4448 East Hall and online via Zoom.

Zoom Webinar Link:
https://umich.zoom.us/j/98734707290