Geodesic
The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum
Informatics and Automation, 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{TRSPY_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 = {Informatics and Automation},
     pages = {87--98},
     publisher = {mathdoc},
     volume = {275},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_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. Informatics and Automation, Classical and modern mathematics in the wake of Boris Nikolaevich Delone, Tome 275 (2011), pp. 87-98. http://geodesic.mathdoc.fr/item/TRSPY_2011_275_a4/