Mathematicians have long known that it’s possible to pack at most 12 identical spheres around and touching a 13th.
In 1943, Hungarian mathematician L. Fejes Tóth conjectured that the optimal arrangement of the surrounding spheres is a highly symmetric pattern based on the 12-faced geometric shape known as a dodecahedron. Sean T. McLaughlin of the University of Michigan in Ann Arbor recently proved this conjecture and described his approach at last month’s Joint Mathematics Meetings in Washington, D.C.