Watercube Beijing and Weaire-Phelan Structure

The Watercube designed for the 2008 Olympics in Beijing is a rare example of a built construction to date using the geometry of foam. The main swimming pool roof in the Watercube has a clear span of 177 metres, demonstrating the strength that this geometry affords for architecture.

The entire structure of the building is based on a unique lightweight-construction derived from the structure of water in the state of aggregation of foam.This same geometry can be found in natural system like crystals,cells and molecular structures.

Watercube gives the impression of random bubbles but it actually uses the Weaire Phelan foam which comprises of just two different cells of equal volume packed together. Underliying the Watercube’s structure is the question concerning the most effective sub-division of three dimensional space with equally sized cells in other word : The maximum cell volume to surface area ratio.

Sub-Division of Three-Dimensional Space

Lord Kelvin posed the problem near the end of the 18th Century: “What shape would soap bubbles in a continuous array of bubbles be?” Plateau had observed in 1873 that when soap bubbles join, there is always a meeting of three surfaces, forming an angle of 120 degrees between their edges. And those edges are always found, four in each corner, with an angle of approximately 109.47 degrees.

In 1887, Lord Kelvin proposed a solution for his own problem based on a 14-sided figure made of 8 regular hexagons and 6 squares. Now, the angle of a square is 90 degrees and a hexagon 120 degrees. Both are far from the 109.47 degrees of Plateau. A regular pentagon has an internal angle of 108 degrees; however dodecahedra (the twelve-sided figure made with regular pentagons) cannot be arranged side by side without leaving a space between them.

Weaire Phelan

It was subsequently supposed that cells composed of combinations of pentagons and hexagons would be more efficient than the foam of Kelvin. However only in 1993, a hundred years after Lord Kelvin’s first tentative answer, did two Irish professors, Weaire and Phelan propose a structure that used less surface than the foam of Kelvin. Their solution utilised two different kinds of cells, a 14-sided one (two hexagons and 12 pentagons) and a 12-sided one (all of pentagons). Both cells have the same volume. In the packing, two irregular pentagonal dodecahedra (12-sided) and six tetrakaidecahedra (14-sided) form a translation unit with a lattice periodicity which is simple cubic.

The foam of the Trinity College physicists Weaire and Phelan has to date not been surpassed as the most efficient subdivision of three dimensional space. Their solution forms the basis for the structure for the National Centre of Swimming of Beijing where the cells are approximately nine metres in diameter.

Despite its apparent complexity and organic form, the Watercube is in fact based on a high degree of repetition. It uses only three different faces (one irregular hexagon, and two different irregular pentagons), four extremities, and three corner configurations.

Conceptually the Watercube’s form derives from a series of Boolean operations where a cuboid is cut from an infinite array of the tightly packed polyhedra. The internal cavity is (actually three internal cavities are) then carved out from this rectangular box leaving just the supporting lattice frame structure. Finally the exposed cell edges are joined at each façade.