The crystalline structure of the resulting solid revealed a lattice structure having five-fold symmetry. When viewed in 3-D, the sample exhibited Icosahedral symmetry. An Icosahedron, one of the five platonic solids, has five-fold and three-fold symmetry. This five-fold symmetry violates the rules of classical crystallography because crystals are formed by a process in which adjacent polygons become attached. In the case of five-fold symmetry, adjacent pentagons cannot be joined without gaps. The lattice formed in the experiment was described as being "quasipriodic", meaning that there was some randomness in its structure that allowed the five-fold symmetry to exist. Because this new substance had some characteristics of crystals, and had a quasiperiodic structure, they were termed quasicrystals. The quasiperiodicity presented a problem - how could it have formed?

Mathematicians observed that quasiperiodicity can be produced in a given dimensionality by taking a cut through a regular lattice of the next higher dimensionality. For the actual quasicrystals, it was found that their five-fold symmetry could be replicated mathematically by taking a cut through a regular six-dimensional lattice. The laws of classical crystallography are satisfied by viewing five-fold (icosahedral) crystals as 3-D hypersurfaces in 6 dimensional space.

This new shape, this five fold (icosahedral configuration), is described by Canadian geometer H.S.M. Coexeter as consisting of 27 points that are evenly distributed over the surface of a 5D sphere in six-dimensional space. The 3D projection of this 27 line figure is called a "Schlafli Double-Six.

These observations beg a very important question. In what way can a dimension greater than three exist? Did some other dimension manifest itself in our three-dimensional space during the test done at the National Institute of Standards and Technology in 1984? Is the beauty of the Schlafli sculpture a result of us getting a glimpse into another dimension?

F.Y.I - Commercially, quasicrystals are being used as heat conductors on food preparation and thawing utensils. Look into Zero-point energy.