4 problems

Lattice-minimality conjecture. This lattice spans at least

For a finite point set in Euclidean three-space, define distinct triangles by congruence classes of triples of distinct points. Three-dimensional three-triangle conjecture. The max…

A finite point set in the plane spans four distinct triangles when its triples of distinct points determine four congruence classes, up to rigid plane isometries. Four-triangle opt…

For an $n$-point set in the plane, let the number of distinct triangles mean the number of congruence classes of triples of distinct points, with triangles identified up to rigid p…