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In other words, we view a fully periodic set, or 'crystal', as a special kind of 'quasicrystal'.
One of the commonly used definitions of a quasicrystal is that of an atomic structure which has a discrete component in its diffraction spectrum.
In particular, they can be viewed as a mathematical abstraction of the set of atomic positions of a physical quasicrystal (at zero temperature, or at a given instant of time).
Does there exist a nice characterization of the 'simplest' aperiodic sets, which might be used to define a notion of 'perfectly ordered quasicrystal'?
This natural quasicrystal exhibits high crystalline quality, equalling the best artificial examples.
Its underlying symmetry is also fivefold but it is not a quasicrystal.
Glotzer and collaborators also hold the record for the densest tetrahedron packing and discovered that hard tetrahedrons can self-assemble into a dodecagonal quasicrystal.
It forms an aperiodic pattern known as a quasicrystal.
In order that the quasicrystal itself be aperiodic, this slice must avoid any lattice plane of the higher-dimensional lattice.
Using mathematics for construction and analysis of quasicrystal structures is a difficult task for most experimentalists.
For a periodic quasicrystal approximant with an 82-tetrahedron unit cell, they obtained a packing density as high as 85.03%.
Recently, he has helped develop a photonic quasicrystal (the quasicrystal analogue of a photonic crystal) for efficiently trapping and manipulating light in selected wavebands.
For a periodic crystal (as opposed to a quasicrystal), the group must also be consistent with maintenance of the three-dimensional translational symmetry that defines crystallinity.
They are remarkable by containing micrometre-sized grains of icosahedrite, a naturally occurring quasicrystal aperiodic, yet ordered structure.
Its discovery followed a 10-year-long systematic search by scientists to find the first natural quasicrystal.