A proof of a dodecahedron conjecture for distance sets (Q2051877)

An \(n\)-point \(s\)-distance set is a set of \(n\) points in a Euclidean space such that the distances between distinct points of the set take precisely \(s\) values. For the particular case of the Euclidean \(3\)-space, the authors show that precisely the vertex sets of regular dodecahedrons are the \(20\)-point \(5\)-distance sets, and that \(20\) is the upper limit for the cardinality of a \(5\)-set.