Calculations of the minimal perimeter for N deformable bubbles of equal area confined to the surface of a sphere

Candidates to the least perimeter partition of the surface of a sphere into N planar connected regions are calculated for N ≤ 32. A search procedure based upon random shuffling and combinatorial enumeration is used. It is conjectured that the optimal configuration for each N > 13 consists of 12 pentagons and N−12 hexagons.