New Maximal Two-Distance Sets

A two-distance set in E is a point set X in the d-dimensional Euclidean space such that the distances between distinct points in X assume only two different nonzero values. Based on results from classical distance geometry, we develop an algorithm to classify, for a given d, all maximal (largest possible) two-distance sets in E. Using this algorithm we have completed the full classification for all d 7, and we have found one set in E whose maximality follows from Blokhuis' upper bound on sizes of s-distance sets. While in the dimensions d 6 our classifications confirm the maximality of previously known sets, the results in E and E are new. Their counterpart in dimension d 10 is a set of unit vectors with only two values of inner products in the Lorentz space R . The maximality of this set again follows from a bound due to Blokhuis. 1997 Academic Press