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. 
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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/

[1] Delone B.N., “Geometriya polozhitelnykh kvadratichnykh form”, UMN, 1937, no. 3, 16–62

[2] Gromov M., Asymptotic invariants for infinite groups, Geometric group theory. V. 2, LMS Lect. Note Ser., 182, eds. G.A. Niblo, M.A. Roller, Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[3] Bogopolskii O.V., “Beskonechnye soizmerimye giperbolicheskie gruppy bilipshitsevo ekvivalentny”, Algebra i logika, 36:3 (1997), 259–272 | MR

[4] Whyte K., “Amenability, bi-Lipschitz equivalence, and the von Neumann conjecture”, Duke Math. J., 99:1 (1999), 93–112 | DOI | MR | Zbl

[5] Papasoglu P., “Homogeneous trees are bilipschitz equivalent”, Geom. Dedicata, 54:3 (1995), 301–306 | DOI | MR | Zbl

[6] Burago D., Kleiner B., “Separated nets in Euclidean space and Jacobians of biLipschitz maps”, Geom. and Funct. Anal., 8:2 (1998), 273–282 | DOI | MR | Zbl

[7] McMullen C.T., “Lipschitz maps and nets in Euclidean space”, Geom. and Funct. Anal., 8:2 (1998), 304–314 | DOI | MR | Zbl

[8] Garber A.I., “O klassakh ekvivalentnosti mnozhestv Delone”, Model. i anal. inform. sistem, 16:2 (2009), 109–118 | MR