The diamond may have a mathematical twinJanuary 7th, 2008 - 4:29 pm ICT by admin
Washington, Jan 7 (ANI): Mathematical analysis of the diamonds structure has led experts to speculate about the possibilities of the existence of a crystal which might have similar properties as that of the diamond.
According to mathematician Toshikazu Sunada, mathematical analysis of the microscopic crystal structure of the diamond has revealed that it has some special symmetric properties, which no other crystal supposedly has.
In fact, out of an infinite universe of mathematical crystals, only one other shares these properties with the diamond - a crystal that researchers call the “K_4 crystal”.
It is known as the K_4 crystal because it is made out of a graph called K_4, which consists of 4 points, in which any two vertices are connected by an edge.
There are especially two properties that help to distinguish the diamond from other crystals.
The first property, called “maximal symmetry”, concerns the symmetry of the arrangement of the building-block graphs, which is maximum in the diamond crystal.
The second special property that the diamond crystal has is called “the strong isotropic property”.
This property resembles 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, in that the crystal looks the same when viewed from the direction of any edge.
Now, it turns out that, out of all the crystals that are possible to construct mathematically, only K_4 shares these two special properties with the diamond.
Although the K_4 crystal presently exists only as a mathematical object, it is tempting to wonder whether it might occur in nature or could be synthesized, said Sunada. (ANI)
Tags: block graphs, crystal structure, crystals, diamond crystal, diamonds, existence, graph, infinite universe, jan 7, mathematical analysis, mathematical object, mathematician, possibilities, rotational symmetry, sphere, twin washington, vertices