Examples of rigid and flexible penny graphs

Abstract

A penny graph is the contact graph of a collection of unit disks and its penny realization is given by the centers of the disks. In this talk we focus on various combinations of rigidity properties of penny graphs and their penny realizations. For instance we present an example of a penny graph which is generically globally rigid, but has two penny realizations. We also consider unit distance graphs and matchstick graphs, which are the graphs that have a unit-distance planar realization. This is joint work with Sean Dewar, Georg Grasegger, Alison La Porta and Anthony Nixon.