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Classification of isosceles 7-point 3-distance sets in 3-dimensional Euclidean space

Authors
Journal
European Journal of Combinatorics
0195-6698
Publisher
Elsevier
Publication Date
Volume
28
Issue
3
Identifiers
DOI: 10.1016/j.ejc.2006.01.003

Abstract

Abstract A subset X in the k -dimensional Euclidean space R k that contains n points (elements) is called an isosceles n -point s -distance set if there are exactly s distances between two distinct points in X and if every triplet of points selected from them forms an isosceles triangle. In this paper, we show that there exist exactly fifteen isosceles 7-point 3-distance sets in R 3 up to isomorphism.

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