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 means 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 analyzing 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.

A "six-dimensional cubic lattice" can be projected onto a three-dimensional Euclidean space so that the lattice points coincide with those of a Quasicrystal. (See en.wikipedia.org/wiki/Quasicrystal and search for "six-dimensional")

A "six-dimensional cubic lattice" can be projected onto a three-dimensional Euclidean space so that the lattice points coincide with those of a Quasicrystal. (See en.wikipedia.org/wiki/Quasicrystal and search for "six-dimensional")

The physics community does 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). The six-dimensional Euclidean space has no connection to string theory or any other theory.
(Updated 7/11/20. -sz}

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