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

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Abstract

A separated net is a set of points which is relatively dense and uniformly discrete (another name for a Delone set). We are dealing with tilings and separated nets in Euclidean spaces and with the question whether a given separated net is biLipschitz to the integer lattice. In this paper we show, as an answer to a question of Burago and Kleiner, that the net that is obtained form the Penrose tiling is biLipschitz to the integer lattice.
Original languageEnglish GB
PublisherarXiv:0711.3707 [math.MG]
StatePublished - 23 Nov 2007

Keywords

  • math.MG
  • math.DS

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