Large simplices determined by finite point sets

Given a set P of n points in ℝd, 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 oned-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. © 2012 The Managing Editors.


Published in:
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 54, 1, 45-57
Year:
2013
ISSN:
2191-0383
Laboratories:




 Record created 2014-07-28, last modified 2018-03-17


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