Summary: In 1989, Erdős conjectured that for a sufficiently large \(n\) it is impossible to place \(n\) points in general position in a plane such that for every \(1 \leq i \leq n - 1\) there is a distance that occurs exactly \(i\) times. For small \(n\) this is possible and in his paper he provided constructions for \(n \leq 8\). The one for \(n = 5\) was due to Pomerance while Palásti came up with the constructions for \(n = 7, 8\). Constructions for \(n = 9\) and above remain undiscovered, and little headway has been made toward a proof that for sufficiently large \(n\) no configuration exists. In this paper we consider a natural generalization to higher dimensions and provide a construction which shows that for any given \(n\) there exists a sufficiently large dimension \(d\) such that there is a configuration in \(d\)-dimensional space meeting Erdős’ criteria.