a. Diagram

                                         Structural Idea

Back in 1887, physicist Lord Kelvin questioned how a three dimensional space could be divided into cells of equal volume with minimal surface area, such as a natural formation of soap bubbles. Kelvin proposed a "foam" consisting of tetrakaidecahedra, a 14-sided polyhedron with six square sides and eight hexagonal sides. It wasn't until 1993 that Weaire and Phelan discovered a more efficient array consisting of two 12-sided polyhedrons and six 14-sided polyhedrons. The steel space frame structure of the Water Cube is essentially the Weaire-Phelan answer to Kelvin's question with a slight twist. To create a more natural look, the template for the space frame was cut out from a rotated array of polyhedrons.

The steel members were encased by a "film" of some 4,000 ETFE (ethylene-tetrafluoroethylene) cushions filled with low-pressure air. ETFE is a special polymer that is one percent the weight of glass and can also transmit more light through its surface. A total of 100,000 square meters (1.1 million square feet) of ETFE were used in the Water Cube. The ETFE cushions improve energy efficiency by allowing solar energy to heat the pools, protect the steel members from the high levels of condensation in the swimming pool environment, and are illuminated by LEDs for impressive displays of changing colors at night.

                                           Cross-sectional Structure Analysis

                        Single Line Structural Diagram

The outer wall is based on the Weaire–Phelan structure, a structure devised from the natural pattern of bubbles in soap lather. In the true Weaire-Phelan structure the edge of each cell is curved in order to maintain 109.5 degree angles at each vertex (satisfying plateau's rules), but of course as a structural support system each beam was required to be straight so as to better resist axial compression. The complex Weaire–Phelan pattern was developed by slicing through bubbles in soap foam, resulting in more irregular, organic patterns than foam bubble structures proposed earlier by the scientist Kelvin.Using the Weaire–Phelan geometry, the Water Cube's exterior cladding is made of 4,000 ETFE bubbles, some as large as 9.14 metres (30.0 ft) across, with seven different sizes for the roof and 15 for the walls.