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Finite or discrete collections of geometric objects. Packings, tilings, polyhedra, polytopes, intersection, arrangements, rigidity.

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The most number of points that realize only $k$ distinct distances

Bannai, Bannai and Stanton proved that $f_d(k) \leq {d + k \choose k}$ in 1983. See: http://link.springer.com/article/10.1007%2FBF02579288 I don't think this bound has been improved in general. It is …
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