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The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
In mathematics, a Meyer set or almost lattice is a relatively dense set X of points in the Euclidean plane or a higher-dimensional Euclidean space such that its Minkowski difference with itself is uniformly discrete.
In this view, a 3D quasicrystal with 8-fold rotation symmetry might be described as the projection of a slab cut from a 4D lattice. The following 4D rotation matrix is the aforementioned eightfold symmetry of the hypercube (and the cross-polytope):
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It can also be called a regular hexdeca-8-tope or hexadecazetton, being an 8-dimensional polytope constructed from 16 regular facets. It is a part of an infinite family of polytopes, called hypercubes. The dual of an 8-cube can be called an 8-orthoplex and is a part of the infinite family of cross-polytopes.
A type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than fermions and bosons. Biexciton: A bound state of two free excitons: Bion: A bound state of solitons, named for Born–Infeld model: soliton Cooper pair: A bound pair of two electrons electron Bipolaron: A bound pair of two polarons
In 1987 Wang, Chen and Kuo announced the discovery of a quasicrystal with octagonal symmetry. [5] The decagonal covering of the Penrose tiling was proposed in 1996 and two years later Ben Abraham and Gähler proposed an octagonal variant for the Ammann–Beenker tiling. [6] Ammann's name became that of the perennial second.
It’s that time of year again when U.S. News & World Report releases their annual best and worst diets list.The panel of experts evaluating the diets comprises 69 specialists in their fields ...