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A counter-example to Kelvin's conjecture on minimal surfaces

1994; Taylor & Francis; Volume: 69; Issue: 2 Linguagem: Inglês

10.1080/09500839408241577

1362-3036

D. Weaire, Robert J. Phelan,

X-ray Diffraction in Crystallography

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 β-tungsten structure. Its surface area is approximately 0.3% less than that of Kelvin's structure.