## Wednesday, May 12, 2010

### Name this polyhedron?

Four years ago, scientists at Pacific Northwest National Laboratory announced their exciting and surprising discovery that gold atoms can also form beautiful polyhedral configurations, like the 16-atom gold molecule shown above. Previously, it had been thought that metals were too reactive to organize themselves in such orderly but hollow structures.

The American Mathematical Society covered the story as follows:

The recently constructed molecular cage, made of 16 gold atoms, has the shape of a truncated tetrahedron.

Add a new member to the family of nano-polyhedra concocted by chemists. This one is made of 16 gold atoms arranged to form a truncated tetrahedron: delete the four vertex atoms from the array corresponding to the tetrahedral number 20. The New York Times for May 16, 2006 reported the construction, which is described in "Existence of hollow golden cages," by Lai-Shen Wang (Pacific Northwest National Laboratory) and collaborators, in the May 30 PNAS. The authors report that this is the first time free-standing metal hollow cages have been detected in the laboratory. In fact their method produced a mixture of the Au16 cages with slightly larger ones made of 17 and 18 atoms. They note that these cages are presently empty, but that their calculations suggest that "these hollow golden cages can easily accomodate a guest atom with very little structural distortion to the host cages." In case you want to do this at home, "The gold cluster anions were produced by using a laser vaporization cluster source" and the results were anyalyzed by photoelectron spectroscopy, "using a magnetic-bottle time-of-flight photoelectron analyzer." No name has been coined yet for these miniature gold cages (inside diameter about 6Å or 6.10-10m) akin to the evocative "buckyball" for the Carbon-60 soccer-ball shaped molecules. In fact the Times's take on the story, written by Kenneth Chang, was "16 Golden Atoms in Search of a Catchy Name."

Work on the properties of the Carbon-60 Buckyball (aka "truncated icosahedron") won the Nobel Prize in physics in 1996. For those who like to play with mathematical ideas playfully, I highly recommend the "Oball" toy shown in the video below, loosely based on the buckyball/truncated icosahedron. We'll have some Oballs on hand during our annual picnic on Memorial Day weekend.

Perhaps work on the golden polyhedral molecules will win a prize as well, but a catchier name than "truncated tetrahedron" might help!