Abstract
We prove that there exist Delone sets in Rd, d≥2, which cannot be mapped onto the standard lattice Zd by Lipschitz co-uniformly continuous bijections satisfying an asymptotic control on the lower distortion. The impossibility of the unrectifiability crucially uses ideas of Lipschitz regular maps recently introduced by M. Dymond, V. Kaluža and E. Kopecká.
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