#weaire-phelan

The Weaire-Phelan structure is an optimal solution to the problem of partitioning space into equal volumes with the least surface area. Denis Weaire and Robert Phelan discovered it in 1993. This structure gained attention due to its efficiency in filling space, offering a configuration that achieves a more balanced distribution of volume and surface area compared to other known structures at the time. Here is my model for the Weaire-Phelan space-filling structure. The Weaire-Phelan structure consists of two different shapes:…

This is a competition entry on the innovative uses of natural stone. Urban Polyhedra aims to organize the natural stone usage, especially on the shores. In the current implementation of this system, random blocks are placed to prevent landslides on the urban coastal areas, but restrict the interaction of the citizens with the shore, and destroy the spaces for sea creatures, and vegetation. Thus, this random placement makes it difficult to interfere with a design/arrangement. Citizens try to reach the…

Becoming popular after the Beijing 2008 Olympics National Aquatics Centre‘s facade (which is believed to be a Voronoi subdivision, as an epic mistake), the Weaire Phelan structure is a solution of equal volumes with minimal surface area. This nice website briefly explains the phenomenon. There is also an implementation on Grasshopper by Jon Mirtschin. Here, I will be modeling the Tetrakaidecahedron of the Weaire-Phelan structure. First, we define the overall size by drawing a 20×10 rhombus. Copy the rhombus by…