Geometry from outer space — Quasicrystal patterning in HYBYCOZO

The 2016 Burning Man installation, Deep Thought, from HYBYCOZO, which was funded an amazing Kickstarter community as well as the Burning Man organization, may be the largest triambic icosahedron ever built.

A what?

A 60 sided regular polyhedron that was over 15 tall and weighed over 3500 lbs (we are checking with the Guinness Book of World Records)

The more interesting aspect of the structure, however, may be that the the pattern on these 60 panels represented what was once thought to be an impossible mathematical concept, the quasicrystal. It was discovered in 2D in the 1970s by Roger Penrose, discovered in 3D by chemist Dan Scheterman winning him the Nobel prize in 2011, and then once again encountered in 2 separate instances on a meteorite site in Russia.

Quasicrystal a form of aperiodic but infinite tiling that lacks translational symmetry.

Say that again?

This ‘forbidden geometry’ was considered so impossible that Dan Scheterman, while researching them in the 1980s, was forced to take a sabbatical from his research group because he was leading to embarrassment and ridicule from the international scientific community.

It was on this sabbatical that he discovered this new state of matter and made a huge stride in material science.

In his own words:

“For a long time it was me against the world,” he said. “I was a subject of ridicule and lectures about the basics of crystallography. The leader of the opposition to my findings was the two-time Nobel Laureate Linus Pauling, the idol of the American Chemical Society and one of the most famous scientists in the world. For years, ’til his last day, he fought against quasi-periodicity in crystals. He was wrong, and after a while, I enjoyed every moment of this scientific battle, knowing that he was wrong.”

Linus Pauling is noted saying “There is no such thing as quasicrystals, only quasi-scientists.” The head of Shechtman’s research group told him to “go back and read the textbook” and a couple of days later “asked him to leave for ‘bringing disgrace’ on the team.”

The Nobel Committee at the Royal Swedish Academy of Sciences said that “his discovery was extremely controversial,” but that his work “eventually forced scientists to reconsider their conception of the very nature of matter.

This concept of pursuing truth against the grain is a very powerful metphor for us HYBYCOZO. It inspires us to follow the path of scientific inquiry and pursue our passions for mathematics and geometry.

The pattern won the Nobel Prize in Chemistry in 2011 and then subsequently was discovered in a meteorite which landed in Russia, proving that this sacred geometry might just have extraterrestrial origins.

Our sculpture and ode to the mathemagicians who stood before us studying the very fabric of mathematics and matter, stands at just over 15 feet tall. It holds 15 people inside.

To imagine how to draw this shape — take each triangle panel of the 20 sided icosahedron (top left) and draw out the center of each triangle until it forms a pyramid (bottom left). This way 1 single panel turn into 3, 20 sides turn into 60.

The image on the bottom left is a Triambic Icosahedron, and at the vertice in the center, 10 panels meet.

This means in 3D space, the polyhedron has 10 fold symmetry, the same as the pattern that was discovered on a meteorite in Russia, with origins dating back to when the planets were first formed.

Impossible in Nature

The “impossible” atomic arrangement which was discovered by Dan Shechtman in 1982 showed a quasi-regularly repeating crystal, a crystalline patterns will fill all available space, but in such a way that the pattern of its atomic arrangement cannot be translated or moved to an area anywhere else. It never repeats.

Thirty years ago, through experiments changing the structure of crystals, laboratories began producing quasicrystals, a strange arrangement of atoms that repeats with two different frequencies rather than one. Rather than a simple ratio of, say, 2:1, the ratio of atoms in a quasicrystal is based on an irrational number, such as the square root of 2:1.

Crystals with these ‘forbidden symmetries’ had been created in the laboratory, but it wasn’t until 2009 that a scientist studying these crystal, and his team reported the first natural quasicrystal.

The first quasicrystal, known as icosahedrite, had a 5-fold atomic symmetry and was discovered in 2009 by a team of researchers led by Professor of Physics at Princeton, Paul Steinhardt and Luca Bindi of the University of Florence.

It was found inside of a 4.57 billion year old meteorite recovered from a remote region of northeastern Russia.

In March of 2015, the researchers discovered another type quasicrystal in a different part of the same meteorite, this one with a decagonal (10-fold) atomic symmetry made from the highly unlikely combination of nickel, iron, and aluminum.

Blink quickly!

Prior to the team finding the first natural quasicrystal in 2009, researchers thought that the structures were too fragile and energetically unstable to be formed by natural processes.

The researchers confirmed that the quasicrystal originated in an extraterrestrial body that formed about 4.57 billion years ago — around the time our solar system formed.

“Until now, quasicrystals were thought to be oddballs, and one of the newest materials formed,” Steinhardt said. “Now we know that is completely wrong. Quasicrystals are one of the first minerals to have formed in the solar system — in the top 250 — long before most of the common minerals found on Earth.”

These findings help answer fundamental questions that are important in all of nature: How do you get really complex arrangements of atoms and molecules from essentially local information? This is a beautiful example of something incredibly rich in structure emerging from very simple rules,” Glotzer said.