Isosceles set

The unique 6-point isosceles set in the plane. The shaded regions show four of the 20 isosceles triangles formed by triples of these points.

In discrete geometry, an isosceles set is a set of points with the property that every three of them form an isosceles triangle. More precisely, each three points should determine at most two distances; this also allows degenerate isosceles triangles formed by three equally-spaced points on a line.