title: Tangency properties of a pentagonal tiling generated by a piecewise isometry.
abstract: Piecewise isometries (PWIs) are known to have dynamical properties that generate interesting geometric planar packings. We analyze a particular PWI introduced by Goetz that generates a packing by periodically coded cells, each of which is a pentagon. Our main result is that the tangency graph associated with this packing is a forest (i.e., has no nontrivial cycles). We show, however, that this is not a general property of PWIs by giving an example that has an infinite number of cycles in the tangency graph of its periodically coded cells.
authors.affiliation: Mathematics Research Institute, School of Engineering, Computer Science and Mathematics, University of Exeter Exeter EX4 4QF, United Kingdom.
authors.forename: Marcello
authors.initials: M
authors.lastname: Trovati
authors.forename: Peter
authors.initials: P
authors.lastname: Ashwin
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008433:Mathematics; D008954:Models, Biological; D008957:Models, Genetic; D015233:Models, Statistical; D008962:Models, Theoretical; D016571:Neural Networks, Computer; D017711:Nonlinear Dynamics