According to the book Space Craft: Developments in Architectural Computing (RIBA Publishing, 2008), > "Irish physicists Denis Weare and Robert Phelan were able to calculate that the most efficient way to divide a space into cells of equal volume while minimizing the surface area between them > was to use a stacked arrangement composed of 75% 14-sided shapes and 25% 12-sided shapes." So far so good, but since the resulting structure would have 22,000 steel members connected at 12,000 nodes, generating an actual model based on the idea exceeded the reach of conventional design.
Instead, according to the book, to manipulate this complex geometric system dynamically, Arup wrote parametric software that automated the drawing and analysis process. Based on specified design constraints and less than 190 loading scenarios, the algorithm iteratively checked the distribution of forces through the entire structure based on specific member sizes, allowing the team to test different design configurations and receive feedback within 25 minutes. > The result was a spectacular building with a sophisticated structure that is optimized in terms of material weight-to-strength ratio, > and it was achieved with relative ease. In addition to the structural advantages, Arup estimated that > it saved $10 million on design costs alone > compared with traditional design methods.