Some history

The foregoing makes a good story, but is not entirely true (I still presume!).
G.E. Kimball had a PhD student Victor A. Lewinson at Columbia before G.F. Neumark. Apart from his thesis there exists a paper [1]. In a way this is a precursor of the "Kimball model". Lewinson and Kimball tried


[1] V. A. Lewinson & G.E. Kimball, J.Chem.Phys. 19(1951)690-693
to apply the "cellular method" by E. Wigner & F. Seitz (1933, successful in the theory of metals) to a computation of the hydrogen molecule. It is documented, that this is not really successful. But the Wigner-Seitz' cell, a polyhedron with the symmetry of the Bravais lattice it is in, might be the archetypal idea of a Kimball sphere.