Weaire–Phelan structure

In 1993, Denis Weaire and Robert Phelan found that this structure was a better solution of the Kelvin problem of tiling space by equal volume cells of minimum surface area than the previous best-known solution, the Kelvin structure.

[1] In two dimensions, the subdivision of the plane into cells of equal area with minimum average perimeter is given by the hexagonal tiling, but although the first record of this honeycomb conjecture goes back to the ancient Roman scholar Marcus Terentius Varro (116-27 BCE), it was not proven until the work of Thomas C. Hales in 1999.

Finally, in 1993, Trinity College Dublin physicist Denis Weaire and his student Robert Phelan discovered the Weaire–Phelan structure through computer simulations of foam, and showed that it was more efficient, disproving the Kelvin conjecture.

[8] In general, it has been very difficult to prove the optimality of structures involving minimal surfaces.

The minimality of the sphere as a surface enclosing a single volume was not proven until the 19th century, and the next simplest such problem, the double bubble conjecture on enclosing two volumes, remained open for over 100 years until being proven in 2002.

Like the hexagons in the Kelvin structure, the pentagons in both types of cells are slightly curved.

[11] Experiments have shown that, with favorable boundary conditions, equal-volume bubbles spontaneously self-assemble into the Weaire–Phelan structure.

[12][13] The associated polyhedral honeycomb is found in two related geometries of crystal structure in chemistry.

[14] Where the components of the crystal lie at the corners of the polyhedra, it is known as the "Type I clathrate structure".

Gas hydrates formed by methane, propane and carbon dioxide at low temperatures have a structure in which water molecules lie at the nodes of the Weaire–Phelan structure and are hydrogen bonded together, and the larger gas molecules are trapped in the polyhedral cages.

[1][15][16] The Weaire–Phelan structure is the inspiration for the design by Tristram Carfrae of the Beijing National Aquatics Centre, the 'Water Cube', for the 2008 Summer Olympics.