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What space-filling arrangement of similar polyhedral cells of equal volume has minimal surface Area? Kelvin proposed the 14-sided Truncated Octahedron. Wearie and Phelan (1994) discovered another 14-sided Polyhedron that has 3% less Surface Area.
References
Gray, J. ``Parsimonious Polyhedra.'' Nature 367, 598-599, 1994.
Wearie, D. and Phelan, R. ``A Counter-Example to Kelvin's Conjecture on Minimal Surfaces.''
Philos. Mag. Let. 69, 107-110, 1994.