In order to create a building structure and ETFE enclosure with the desired references to liquid, the team members explored the geometry of soap bubbles, studying the work of Irish physicists Denis Weaire and Robert Phelan. In 1993, the pair proposed a solution to the so-called Kelvin problem (named after late 19th-century British mathematician William Thomson Kelvin) that asks how to divide space into an equal number of cells with the least surface area between them. Weaire and Phelan's "foam" is made up of a combination of polyhedra with either 14 or 12 faces. Despite its regularity, the honeycomblike structure was well suited to the team's goals because "when viewed at an arbitrary angle, it appears totally random and organic," says Tristram Carfrae, leader of the group of engineers from Arup.

	VENTED CAVITY: TYPICAL OPERATION 1. Fresh external air circulates within cavity. 2. ETFE pillows perform like a greenhouse enclosure. 3. Controlled daylight and radiant heat illuminate and passively heat pool. 4. Operable ETFE switches on or off to shade interior. 5. Fan-assisted, preheated fresh air is returned to pool.
With the exception of the elimination of operable shading, the Water Cube's cavity wall was realized almost unchanged from the competition entry scheme. Drawing courtesy ARUP

Although Weaire and Phelan's foam forms the basis of the structure, there is only one spot in the building where their "pure" geometry is clearly recognizable-the second-floor Bubble Bar. Here, a collection of ETFE-clad polyhedra encloses a room where visitors can sip champagne.

Elsewhere in the building, the underlying geometry is hard to discern because of the team's form-finding process. In order to develop a building structure from the theoretical foam structure, the designers from CCDI wrote a script that would allow them to assemble an infinite array of the Weaire-Phelan units, rotate it in three dimensions, and then slice the packed cells to create a box 584 feet square in plan and 102 feet tall. They then removed three interior volumes for halls devoted to swimming and diving competitions, the pool for water polo, and the leisure center. From the foam left behind after this virtual cutting and deconstruction process, they created a space frame by replacing the edges of the polyhedra with steel tubes that meet at spherical nodes. They decided to encapsulate the space frame in 4,000 bubblelike, air-filled ETFE pillows to create a vented cavity 12 feet wide within the walls and one that is 25 feet deep within the roof, protecting the steel structure from the corrosive humidity of the pool environment.

During the day, diffuse sunlight provides much of the lighting for the Water Cube's interior spaces, such as the competition pool (right). At night, the building becomes a glowing blue box (below) with the help of LEDs. Photo © Iwan Baan (top); PTW (below)

The result is a seemingly irregular, but in actuality a rigorous and buildable structure-and-building-envelope combination appropriate for earthquake-prone Beijing. The on-site welded space frame, with column-free spans of up to 396 feet, is highly efficient, nonlinear, nondirectional, and remarkably stable. The ETFE cladding, which weighs just 1 percent of an equivalent glass panel, contributes to the building's seismic performance, since it helps reduce the gravity and lateral loads that the structure would be subject to during a temblor, explains Carfrae.

As the basis of the building structure, the design team studied the work of physicists Denis Weaire and Robert Phelan. The pair proposed a honeycomblike structure made up of polyhedra with either 14 or 12 faces (left) as the solution to the so-called Kelvin problem. The designer team assembled an infinite array of these cells, rotated them in three dimensions, and then sliced them to create a box 584 feet square in plan and 102 feet tall (right). The second-floor Bubble Bar (bottom) is the only place in the Water Cube where Weaire and Phelan's "pure" geometry is still visible. Photo courtesy PTW (bottom); PTW/China State Construction Engineering (top left); illustration: ARUP (top right)