Princeton Chemist Solves a Problem With Space(200)A chemist at Princeton University has tackled an ancient geometrical problem—the solution of which should have an incredible effect on architecture, or Tetris.

The original problem was as frustrating as it was simple: How do you fill a three-dimensional space with objects that aren’t cubes? Imagine packing your dishes before a move: No matter how Type A your packing job, there’s going to be lots of unused, wasted space between the dishes and cups. Or playing Tetris with a z-axis. But Princeton chemist Salvatore Torquato and his colleagues discovered that for certain combinations of shapes, there doesn’t have to be.

Torquato discovered an arrangement of octahedra and tetrahedra that efficiently fills a cubic space—and can be repeated infinitely. Princeton blogger Gale Scott reports:

The researchers' work involves "tiling," also known as "tessellation" after the Latin word "tessella," meaning a small cube or tile. Just as someone tiling a floor repeats a geometric pattern to fill the length and width of the floor space, Torquato and colleagues take that task to a third dimension, adding height and filling the whole room. That process involves fitting more complex three-dimensional "tiles" together, in this case the regular octahedron (a solid figure with eight triangular faces) and the regular tetrahedron (a figure with four triangular faces).

A professor at the Princeton Institute for the Science and Technology of Materials and Princeton Center for Theoretical Science, Torquato follows in the footsteps of architect R. Buckminster Fuller, who described the structural configuration of two regular tetrahedral and a single regular octahedron as an octet truss. That geometrical innovation—or discovery—has since influenced everything from space-frame roofing to the tube-frame chassis on Ducati motorcycles.

(Credit where credit is due: Alexander Graham Bell discovered—or invented—the space frame at the start of the 20th century, a structural innovation that Fuller won acclaim for realizing in the 1950s. Bell was a devoted kite-maker, and he worked to apply some of the structural concepts behind his rather fabulous kites to nautical engineering. He was mostly unsuccessful in this arena.)

So what does Princeton’s discovery have to do with architecture? Plenty of architects use triangle-y forms—Preston Scott Cohen comes to mind, with his Herta and Paul Amir Building for the Tel Aviv Museum of Art—but the greatest application will come to materials science and developing stronger structures.

Seeing the solution, it’s hard to believe that it was ever a problem. Tetris, however, remains difficult.