I love quasicrystals—like crystals, but with patterns that never repeat, like Penrose tiles. But they’ve very rare in nature. They’re created only by the most exotic and violent events: a high-speed collision of asteroids, lightning hitting a downed power cable in a sand dune—or an atomic bomb!

Amazingly, the first 3 kinds of naturally occurring quasicrystal were discovered in a single meteorite that landed in Khatyrka, in the far east of Russia. They’ve never been found anywhere else! And this meteorite is highly anomalous: it’s the only meteorite known that contains metallic aluminum—and it seems to have been formed in a ultra-high-velocity collision between asteroids.

The only other quasicrystal I know that may be naturally created came from a bolt of lightning hitting a sand dune near a downed power cable in Nebraska. Then there was one found amid the fused desert sand and copper transmission cable left behind by the first atomic bomb test at Trinity, New Mexico. That’s not quite ‘naturally created’.

And that’s all. As far as I can tell, the rest have been made in labs!

Here are the 3 kinds of quasicrystal found in the Khatyrka meteorite, in order of their discovery:

• Icosahedrite, Al₆₃Cu₂₄Fe₁₃. By the way, these numbers are percentages, since quasicrystals don’t have integer-ratio molecular formulas the way conventional compounds do, due to their aperiodic nature.

Icosahedrite has full three-dimensional icosahedral symmetry and is quasiperiodic in all 3 directions. The easiest way to describe it mathematically is the ‘slice and project’ method. You start with a lattice in 6 dimensions, choose a 3d slice, thicken that up a bit, take the lattice points that lie in this slice, and project them down to 3d space. The lattice in 6 dimensions is called the D₆ lattice: it consists of those 6-tuples of integers that sum to an even integer. If we slice along the correct 3d subspace the result has icosahedral symmetry. A lot of math in this mineral!

• Decagonite, Al₇₁Ni₂₄Fe₅. This a ‘stacked’ quasicrystal: quasiperiodic with tenfold rotational symmetry in two dimensions, and ordinary periodic stacking in the third direction. We can build the 2d pattern using the slice and project method starting from the A₄ lattice in 4 dimensions. The A₄ lattice, in turn, is gotten by taking 5-tuples of integers, but only those that sum to zero. This quasicrystal looks like this:

• i-Phase II, Al₆₂Cu₃₁Fe₇. Like icosahedrite this has full icosahedral symmetry and you get it mathematically using the slice-and-project method starting from the D₆ lattice. But it has a distinctly different composition: more copper and less aluminum. It’s the first quasicrystal composition discovered in nature before being made in the lab.

The Nebraska quasicrystal shows how blurry the concept of ‘natural’ can be. It was found inside a ‘fulgurite’: a rock made when lightning hits sand. They found it in the Sand Hills near Hyannis, Nebraska, near a downed power line during a storm. It’s unclear whether this fulgurite was created by a lightning strike or by the falling power line creating its own arc, so the ‘natural vs manmade’ status is genuinely ambiguous.

What’s more important is it was a new kind of quasicrystal produced by a high-current, high-temperature, rapid-quench event on Earth’s surface! It has a composition of roughly Mn_72.3Si_15.6Cr_9.7Al_1.8Ni_0.6. Its atomic planes have 12-fold symmetry in a nonrepeating pattern, and these planes are stacked periodically along the perpendicular direction.

Here’s a picture of this quasicrystal:

References

On icosahedrite, the first natural quasicrystal to be found in the meteorite from Khatyrka:

• L. Bindi, J. M. Eiler, Y. Guan, L. S. Hollister, G. MacPherson, P. J. Steinhardt and N. Yao, Evidence for the extraterrestrial origin of a natural quasicrystal, Proceedings of the National Academy of Sciences 31 (2012), 1396-401.

On decagonite, the second to be found:

• I. Buganski and L. Bindi, Insight into the structure of decagonite—the extraterrestrial decagonal quasicrystal, IUCrJ 8 (2021), 87–101.

On i-phase II, which is the provisional designation of the third quasicrystal found in that meteorite:

• L. Bindi, C. Lin, C. Ma and P. J. Steinhardt, Collisions in outer space produced an icosahedral phase in the Khatyrka meteorite never observed previously in the laboratory, Scientific Reports 6 (2016), 38117.

On the dodecagonal quasicrystal found in the dune in Nebraska:

• L. Bindi, M. A. Pasek, C. Ma, J. Hu, G. Cheng, N. Yao, P. D. Asimow, and P. J. Steinhardt, Electrical discharge triggers quasicrystal formation in an eolian dune, Proceedings of the National Academy of Sciences 120 (2023), e2215484119.

On the quasicrystal found at the atomic bomb test site:

• L. Bindi, W. Kolb, G. N. Eby, P. D. Asimow, T. C. Wallace and P. J. Steinhardt, Accidental synthesis of a previously unknown quasicrystal in the first atomic bomb test, Proceedings of the National Academy of Sciences 118 22 (2021), e2101350118.

This has icosahedral symmetry, but it’s quite different than the other quasicrystals I’ve mentioned, since it’s mostly made of silicon! Its formula is Si₆₁Cu₃₀Ca₂Fe₂.

This entry was posted on Thursday, May 14th, 2026 at 9:40 am and is filed under chemistry, mathematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.