Packing regular triplets of circles on a sphere

Abstract

This article examines how 3 N non-overlapping equal circles forming N triplets must be packed on a sphere to ensure that the angular diameter of the circles will be as large as possible. Furthermore, this problem is solved under the constraint that, within each triplet, the circle centres lie at the vertices of an equilateral triangle inscribed into a great circle of the sphere. Computer-generated solutions to this optimization problem are presented for N =2–7 triplets. The configurations obtained are characterized as compounds (nolids) of equilateral triangles.