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A separated net is a set of points which is relatively dense and uniformlydiscrete (another name for a Delone set). We are dealing with tilings andseparated nets in Euclidean spaces and with the question whether a givenseparated net is biLipschitz to the integer lattice. In this paper we show, asan answer to a question of Burago and Kleiner, that the net that is obtainedform the Penrose tiling is biLipschitz to the integer lattice.

The net created from the Penrose tiling is biLipschitz to the integer lattice