Forma, Vol. 11 (No. 3), pp. 209-213, 1996

A Counter-Example to Kelvin's Conjecture on Minimal Surfaces

D. Weaire and R. Phelan

Department of Pure and Applied Physics, Trinity College, Dublin 2, Ireland

(Received December 10, 1993; Accepted December 17, 1993)

Abstract. Kelvin's conjecture, that a b.c.c. arrangement of his minimal tetrakaidecahedron divides space into equal cells of minimum surface area, has stood for over one hundred years. We have found a counter-example, in the form of a structure analogous to that of some clathrate compounds and also related to the b-tungsten structure. Its surface area is approximately 0.3% less than that of Kelvin's structure.