A set of n-lattice points in the plane, no three on a line and no four on a
circle, such that all pairwise distances and all coordinates are integral is
called an n-cluster (in R2). We determine the smallest existent
7-cluster with respect to its diameter. Additionally we provide a toolbox of
algorithms which allowed us to computationally locate over 1000 different
7-clusters, some of them having huge integer edge lengths. On the way, we
exhaustively determined all Heronian triangles with largest edge length up to
6⋅106.Comment: 18 pages, 2 figures, 2 table