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2. Crystallographic point group - Wikipedia

   en.wikipedia.org/wiki/Crystallographic_point_group

   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 ...

3. Torus interconnect - Wikipedia

   en.wikipedia.org/wiki/Torus_interconnect

   3D Torus: three dimensions, the nodes are imagined in a three-dimensional lattice in the shape of a rectangular prism, with each node connected with its six neighbors, with corresponding nodes on opposing faces of the array connected. Each edge consists of n nodes. communication can take place in six directions, +x, −x, +y, −y, +z, −z ...

4. Laves graph - Wikipedia

   en.wikipedia.org/wiki/Laves_graph

   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.

5. DNA nanotechnology - Wikipedia

   en.wikipedia.org/wiki/DNA_nanotechnology

   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.

6. Crystal structure - Wikipedia

   en.wikipedia.org/wiki/Crystal_structure

   The fourteen three-dimensional lattices, classified by lattice system, are shown above. The crystal structure consists of the same group of atoms, the basis, positioned around each and every lattice point. This group of atoms therefore repeats indefinitely in three dimensions according to the arrangement of one of the Bravais lattices.

7. Layer group - Wikipedia

   en.wikipedia.org/wiki/Layer_group

   In mathematics, a layer group is a three-dimensional extension of a wallpaper group, with reflections in the third dimension.It is a space group with a two-dimensional lattice, meaning that it is symmetric over repeats in the two lattice directions.

8. Ice-type model - Wikipedia

   en.wikipedia.org/wiki/Ice-type_model

   The partition function also counts the number of nowhere-zero 3-flows. [6] For two-dimensional models, the lattice is taken to be the square lattice. For more realistic models, one can use a three-dimensional lattice appropriate to the material being considered; for example, the hexagonal ice lattice is used to analyse ice.

9. Lattice (group) - Wikipedia

   en.wikipedia.org/wiki/Lattice_(group)

   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 ...