The challenge of three dimensional packing is a classic mathematical problem dating back to the times of Plato and one developed by Archimedes, Newton, and countless other classical thinkers. Our research focuses on the specific 3-D packing problem of irregular polyhedral networks in natural foaming systems. Foaming networks are inherently efficient in terms of material usage while maintaining strength in all directions.

Networks in foaming systems are defined by the radical plane, which is described as the precise location and angle of the boundary plane between two spheres resulting in a system of polyhedra. This network informs all foaming systems in nature- from the structure of bones, to the froth in a freshly poured beer. Assuming a system of non-uniform sphere radii and locations, our algorithm describes an irregular polyhedral network, where each sphere’s resulting polyhedra’s size and location is determined by the size and location of all other three dimensionally packed spheres in the dataset.

The implications of this research in architecture are complicated to conceptualize because the modern world exists primarily in stacked space. Some of the immediate benefits include the ability to cantilever and span great distances thanks to the seemingly endless vectors of lateral bracing- all while utilizing the smallest amount of material possible. Foam’s spatial development also creates multi-adjacencies between polyhedra; the average number of sides for each polyhedron in a foaming network is between eleven and seventeen.

We fabricated the physical model using selective laser sintering (SLS) techniques. It is a composite of fused nylon, acrylic and epoxy.

Work published in: Research & Design 2: Textile Tectonics- In collaboration with Dave Beil and under instruction of Lars Spuybroek.