A remarkable eight-point planar configuration Original Research Article

There is a unique eight-point planar configuration H8 in which each point has exactly three distinct distances to the other seven, and it is the only eight-point configuration that minimizes the sum of the points’ distance counts. The points in H8 are the vertices of two same-centered squares at a rotation of 45° with side-lengths ratio 2 cos 15°. I first heard about H8 from Paul Erdős, who heard about it from Heiko Harborth.