Kelvin's conjecture on minimal froths and the counter-example of Weaire and Phelan

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Abstract
Weaire and Phelan's recent discovery of a clathrate structure (that of β-tungsten) as an ordered minimal froth (space-filling assembly of polyhedral bubbles) with less surface per unit volume than Kelvin's b.c.c. arrangement of truncated octahedra suggests searching among other known tetrahedrally close-packed crystalline phases for a structure with even less surface per unit volume. Two possible candidates are proposed, the α-phase (β-uranium) and the T-phase of Bergman, Waugh and Pauling (1957, Acta crystallogr, 10, 254). A general expression for the energy of tetrahedrally close-packed structures with equal bubble volume is given.