Quasicrystals

One of the undergraduate series of lectures that I attended at PCMI was on Geometry and Quasicrystals, given by Marjorie Seneschal, math professor at Smith College in Massachusetts. She's written a book on the subject, "Quasicrystals and Geometry".

We even built a quasicrystal out of Zometools at PCMI. The largest quasicrystal ever built - according to Marjorie Senechal. One evening after dinner we got into several groups. Each group built the following piece. It consists of a green tetrahedron hanging in the middle, surrounded by a blue icosahedron, and finally a red rhombic triacontahedron.

Here is a view of just the outer polyhedron almost finished.

Finally, some of the undergraduates, who were experts at Zometools, put all these building blocks together in a large quasicrystal.

And this was the result

This is a model of a "binary icosahedral Cd-Yb quasicrystal." The amazing thing is that anyone was able to figure out this structure. Here is a short description of how they did it.

Zometools are a lot of fun, and I recommend getting a set and having fun.

PS. For those of you who have been wanting to know: a soccer ball is a truncated icosahedron.

Update: Of course, an excellent source of information about quasicrystals is at the Nobel Prize website, since Dan Schechtman won the Chemistry prize in 2011 for his discovery of quasicrystals back in 1982. On that site there is a link "Popular Information," which leads to a nice 7-page paper with excellent graphics explaining crystals and quasicrystals.

Update 2: More information here.