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The regular skew polyhedron onto which the Laves graph can be inscribed. The edges of the Laves graph are diagonals of some of the squares of this polyhedral surface. As Coxeter (1955) describes, the vertices of the Laves graph can be defined by selecting one out of every eight points in the three-dimensional integer lattice, and forming their nearest neighbor graph.
A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...
In crystallography, a crystallographic point group is a three dimensional point group whose symmetry operations are compatible with a three dimensional crystallographic lattice. According to the crystallographic restriction it may only contain one-, two-, three-, four- and sixfold rotations or rotoinversions. This reduces the number of ...
The conceptual foundation for DNA nanotechnology was first laid out by Nadrian Seeman in the early 1980s. [2] Seeman's original motivation was to create a three-dimensional DNA lattice for orienting other large molecules, which would simplify their crystallographic study by eliminating the difficult process of obtaining pure crystals.
The seven lattice systems and their Bravais lattices in three dimensions. In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (), [1] is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by
De Bruijn showed that Penrose tilings can be viewed as two-dimensional slices of five-dimensional hypercubic structures; [48] similarly, icosahedral quasicrystals in three dimensions are projected from a six-dimensional hypercubic lattice, as first described by Peter Kramer and Roberto Neri in 1984. [49]
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