Large simplices determined by finite point sets

@inproceedings{Moric2012LargeSD,
  title={Large simplices determined by finite point sets},
  author={Filip Moric},
  year={2012}
}
Given a set P of n points in R, let d1 > d2 > . . . denote all distinct inter-point distances generated by point pairs in P . It was shown by Schur, Martini, Perles, and Kupitz that there is at most one d-dimensional regular simplex of edge length d1 whose every vertex belongs to P . We extend this result by showing that for any k the number of d-dimensional regular simplices of edge length dk generated by the points of P is bounded from above by a constant that depends only on d and k. 

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