What makes a diamond a diamond? What is it that captivates and entrances human beings about diamonds? And what accounts for the beauty of a clear diamond crystal?
A mathematician, Toshikazu Sunada explains some secrets of the diamond’s beauty in an article which recently appeared in the Notices of the American Mathematical Society. These secrets can be discovered by a mathematical analysis of its microscopic crystal structure. It appears this structure has some very special, and unique symmetric, properties.
The diamond crystal has two special properties that distinguish it from other crystals. Firstly there is what is called “maximal symmetry”, which is the symmetry of the arrangement of the building-block graphs.. Some crystals have better symmetry than other but it appears the diamonds have the best of all. The diamond also has a second special property called “the strong isotropic property”.
This property is best described as the rotational symmetry that characterizes the circle and the sphere: No matter how you rotate a circle or a sphere, it always looks the same. The diamond crystal has a similar property.
No matter where you look in the diamond crystal it looks the same from any viewpoint. In fact, if you rotate the diamond crystal from the direction of one edge to the direction of a different edge, and it will still look the same.
So it is a diamond that makes a diamond and it is the symmetry, to put it very basically, that gives it that wonderous clear beauty we know so well. Sunada’s article, “Crystals That Nature Might Miss Creating”, is appearing in the February 2008 issue of the AMS Notices and will be posted online January 3.
