The 2011 Nobel Prize in Chemistry was awarded for the discovery, in 1982, of Quasicrystals.
Normal crystals have a periodic structure in 3D space. This meant that if the crystal lattice was translated without rotation, so that one point of the moved lattice line was aligned with the position of a corresponding point of the old position, then every point of the new lattice would line up with some point of the old position. Quasicrystals have a non-periodic structure in 3D. This means that the stated condition is not true for the Quasicrystal.
A standard method of analysing crystals involved bouncing electrons off of them and studying the resultant patterns. Such patterns did not result from bouncing electrons off of glass or liquids, only off of crystals. When this procedure was applied to Quasicrystals, it revealed sharp points characteristic of crystals.
Quasicrystals produce patterns of sharp points, as crystals do, but the symmetry of these points is forbidden in 3D space. It is known that there is a mathematical construction that takes a "six-dimensional hypercubic lattice" from six-dimensional Euclidean space and projects the lattice points to three-dimensions Euclidean space so that these points coincide with that of a Quasicrystal. (See en.wikipedia.org/wiki/Quasicrystal and search for "six-dimensional")
Mainstream physicists do not attach any physical significance to this mathematical fact since our space is considered to be three-dimensional (or four-dimensional if relativistic space-time is considered). Nor does a six-dimensional Euclidean space have any connection to string theory with its compactified dimensions.
In my own theory, the mathematical fact of projection from six to three Euclidean dimensions translates directly to a physical arrangement of atomic centers in six dimensions. My theory is called A Unified Field Theory in 6 Euclidean Dimensions Plus Absolute Time (UFT6). It was conceived long before Quasicrystals were discovered.
I consider Quasicrystals to be evidence in favor of a 6D space, and of UFT6. Such evidence, of course, is not proof that 6D space exists. But it is dramatically simpler than the lengths one must go to to explain Quasicrystals in only three dimensions.
(This post was updated and moved on 11/6/2014. -sz)