What space-filling arrangement of similar cells of equal volume has minimal surface area? This questions arises naturally in the theory of foams when the liquid
content is small. Kelvin (Thomson 1887) proposed that the solution was a 14-sided
truncated octahedron having a very slight
curvature of the hexagonal faces.
while Kelvin's slightly curved variant has a slightly less optimal quotient of 0.757.
Despite one hundred years of failed attempts and Weyl's (1952) opinion that the curved truncated octahedron could not be improved
upon, Weaire and Phelan (1994) discovered a space-fillingunit cell consisting of six 14-sided polyhedra and two
12-sided polyhedra with irregular faces and only hexagonal faces remaining planar.
This structure has an isoperimetric quotient
of 0.765, or approximately 1.0% more than Kelvin's cell.
The building for water events at the 2008 Beijing Olympics had a structure based on Weaire-Phelan foam (Rehmeyer 2008, Beijing Organizing Committee of the Olympiad 2008).
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