Geodesic
The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 87-98

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It is proved that the family of bi-Lipschitz classes of Delone sets in Euclidean space of dimension at least $2$ has the cardinality of the continuum. 
@article{TM_2011_275_a4,
     author = {A. N. Magazinov},
     title = {The family of {bi-Lipschitz} classes of {Delone} sets in {Euclidean} space has the cardinality of the continuum},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {87--98},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_275_a4/}
}
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A. N. Magazinov. The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 87-98. http://geodesic.mathdoc.fr/item/TM_2011_275_a4/