Combinatorial and metric properties of polyhedrons at the edges
In the thesis, I research the properties of convex polyhedrons that occur by repeatedly cutting all the peaks of a general polyhedron in such a way that the cuts can only cut edges from the tip. The development lines generated by this process are composed of simple polyhedrons. In my thesis I analyze the metric and combinatorial properties of these polygons and polyhedrons and show that the sheet structure of the resulting convex body exhibits fractal properties. With regard to the latter, I point out the visual analogy between the flat network of polyhedrons and the flat foams. The described process may have other physical applications, as I will show that this is the geometric formulation of Redner and Krapivsky’s wear model. Finally, I will also briefly introduce the dual process, which creates symplicial polyhedrons.