On an abrasion motivated fractal model

Abstract

In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping.