James Allen News Center

A Japanese mathematician thinks he may have discovered a crystal which might have similar properties as that of the diamond.

Toshikazu Sunada has reported that a careful mathematical analysis of the microscopic crystal structure of the diamond shows that it features symmetric properties that no other crystal possesses.

Out of an infinite universe of mathematical crystals, there is just one that shares properties with the diamond. This is a crystal that researchers call the K_4 crystal. It has this name because it is made from a graph called K_4. This consists of four points, where any two vertices are connected by an edge.

The mathematician reports that there are two properties that set a diamond apart from other crystals. First, maximal symmetry, which is the symmetry of the arrangements of the building-block graphs. He says that this is at the maximum in the diamond crystal.

Next is the fact that the diamond crystal has the strong isotropic property. This resembles the rotational symmetry of a circle and a sphere. Any way you rotate a circle or sphere, it always looks identical. Diamond crystals have such a property as well – the crystal looks the same when viewed from the direction of any edge.

According to Sunada, of all possible crystals you can construct mathematically, just the K_4 shares these unique properties with the diamond.