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These Things Are So Pretty. They Must Be Useful, Too. Right?

Source: Stan Schein and James Maurice Gayed/University of California Los Angeles via PNAS

Goldberg polyhedra, introduced in the Proceedings of the National Academy of Sciences in February. They are the first such convex polyhedra discovered in more than 400 years, here visualized by the authors using UCSF Chimera software.  Close

Goldberg polyhedra, introduced in the Proceedings of the National Academy of Sciences... Read More

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Source: Stan Schein and James Maurice Gayed/University of California Los Angeles via PNAS

Goldberg polyhedra, introduced in the Proceedings of the National Academy of Sciences in February. They are the first such convex polyhedra discovered in more than 400 years, here visualized by the authors using UCSF Chimera software. 

Having a young daughter brings you into daily contact with things that aren't immediately useful but are "real pretty." It's just like covering sustainability.

3D-shapes week in kindergarten rolled by recently, and a colorful menagerie of flattened polyhedra came home in the school folder.

The same week also featured a study about 3-D shapes in the Proceedings of the National Academy of Sciences. The journal unveiled a group of round-looking things, newly discovered polyhedra, which the authors named after the late mathematician Michael Goldberg. All the edges are the same length. All the faces are flat, and when they're 'arranged' the right way, they end up approximating a sphere. The angles aren’t all equal, but you can’t have everything.

They belong to a larger class of lovely little things that is so exclusive the last time somebody stumbled onto new ones was astronomer Johannes Kepler in 1611. Plato, or people calling themselves Plato, discovered five forms that have equal sides, equal angles and identical polygonal faces. Archimedes in the third century BC widened the definition and found 13 more shapes. Think soccer ball.

But What’s It Do?

The last line of the new study caught my attention: "These polyhdedra could be useful in applications requiring structures that approximate spheres."

Now that I understand. It's a familiar intention: Look at this pretty thing in the world -- how the sun shines, how the wind blows, how the water flows. Let's use that for something other than staring at agape.

It’s all a part of the biomimetic instinct, the drive to blend nature’s utility and beauty into our own works. In a recent New Yorker article about humanity's quest to mimic and control fusion energy, which is what makes the Sun hot, physicist Ned Sauthoff of Oak Ridge National Laboratory said the wish to harness the Sun probably goes back to a caveman who, stepping outside into sunlight one day, "was impressed by the warmth and the light, and, being human, he said, 'How can I have one of those?'"

Sustainability is all about comparing our crude inventions with what might be called, for lack of a better phrase, "the basic fabric of the Universe," and coming away informed enough to mimic or replicate it.

Circling the Square

The history of architecture is largely a history of squares, rectangles, cubes and shoeboxes. Humans have long built things to stand straight up. That makes Western architecture a fight against gravity hundreds, even thousands, of years old.

It needn’t be that way. Buckminster Fuller, the futurist and famed builder of geodesic domes, popularized the idea that non-rectilinear structures built up from edges and vertices -- “struts and nodes” to architects -- can take care of gravity as easily as or better than our world of right angles.

Geometry can be a source of structural ideas for designers and architects even independent of the material a building might be made of. “The geometry of any building system overwhelms all the other constraints that go into making a building,” James Maurice Gayed, a co-author and UCLA researcher, said in an email.

Let It Grow

Peter Jon Pearce has spent his architectural and design career studying the basic fabric of the Universe -- in biology, crystallography, metallography, physics. Some of Pearce's best-known work includes Biosphere 2, Las Vegas’s Fremont Street canopy and the family pavilion and exhibition hall at Chicago's Navy Pier. Pearce spent the latter half of the 1960s and the 1970s developing “first principles” by which designers might learn to adapt geometry and structures found in nature, where energy and resource efficiency rule the day.

"I was interested in energy efficiency back in the early '60s,” Pearce said in an interview. “It just seemed like the logical thing to do.” At that time his inspiration was more European auto racing than the bubbles, dried mud and dragonflies pictured on his website.

The fabric of the universe isn’t limited to static structures, Pearce said. In fact, nature likes to grow and fill space. It likes to pick shapes that are infinitely repeatable and combine them into larger structures. Most polyhedra, including these new ones, won’t fit together as snugly or as obviously as the bubbles created when you blow milk through a straw.

How Can I Have One?

I sent Pearce the PNAS paper, to weigh in on its potential use in architecture. Can we build spectacular Olympic stadiums from these designs? Should office buildings be round? As Sauthoff put it, how can I have one of those?

The shapes "can't be combined to form repeating structures," Pearce said. Like the forms called icosahedra, the Goldberg polyhedra might lead to dome-structures and not much else. “I see no particular benefits for large-scale structure design” in the new forms, he said in an email.

Besides, much of mainstream architecture has yet to incorporate geometric innovations that have already been around a while, which makes even many of today's designers really, uh, square. The profession has “a disheartening lack of interest in high-performance design -- [in] what is now loosely referred to as sustainability,” Pearce wrote in a 2006 essay. "Certainly many of the most iconic architects of our day continue to exhibit little interest in design for sustainability."

Good News for a Change

Regardless of whether a future Olympic host sees fit to build the Goldberg polyhedra into a soccer stadium (or even into a soccer ball), Gayed and Stan Schein, a UCLA professor and co-author, see far-ranging possibilities for the near-spheres.

“We are NOT suggesting that buildings should be made of domes and spheres, as Fuller popularised,” Gayed said in an email. Instead, they are offering a novel suggestion for designers, materials scientists or architects potentially in need of one.

Architecture is so large-scale, it's a challenging place to start thinking practically about new geometry. Practical uses for polyhedra might instead come from the manufacture of much smaller things. As 3D-printing comes on line, shapes like the Goldberg polyhedra, which have easy-to-build components, might eventually be useful in chip design, materials science and even education, the authors suggest. Near-spherical computer monitors built from one or another Goldberg polyhedron could be used to display climate change data in schools and elsewhere.

“Geometry,” Gayed says, “will become a part of the ‘tool kit’ that engineers use to make manufacturing more efficient, less costly and far more productive.”

And real pretty.

More by Eric Roston (@eroston on Twitter):

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