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  2. Miller index - Wikipedia

    en.wikipedia.org/wiki/Miller_index

    Planes with different Miller indices in cubic crystals Examples of directions. Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h, k, and ℓ, the Miller indices.

  3. Hexagonal lattice - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_lattice

    The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices. In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb ...

  4. Brillouin zone - Wikipedia

    en.wikipedia.org/wiki/Brillouin_zone

    The boundaries of this cell are given by planes related to points on the reciprocal lattice. The importance of the Brillouin zone stems from the description of waves in a periodic medium given by Bloch's theorem , in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone.

  5. Hexagonal tiling - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_tiling

    The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter. The optimal three-dimensional structure for making honeycomb (or rather, soap bubbles) was investigated by Lord Kelvin, who believed that the Kelvin structure (or body-centered cubic lattice) is ...

  6. Lattice plane - Wikipedia

    en.wikipedia.org/wiki/Lattice_plane

    In crystallography, a lattice plane of a given Bravais lattice is any plane containing at least three noncollinear Bravais lattice points. Equivalently, a lattice plane is a plane whose intersections with the lattice (or any crystalline structure of that lattice) are periodic (i.e. are described by 2d Bravais lattices). [ 1 ]

  7. Lattice (group) - Wikipedia

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

    In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.

  8. Voronoi diagram - Wikipedia

    en.wikipedia.org/wiki/Voronoi_diagram

    A body-centred cubic lattice gives a tessellation of space with truncated octahedra. Parallel planes with regular triangular lattices aligned with each other's centers give the hexagonal prismatic honeycomb. Certain body-centered tetragonal lattices give a tessellation of space with rhombo-hexagonal dodecahedra.

  9. Hexagonal crystal family - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_crystal_family

    In particular, there are crystals that have trigonal symmetry but belong to the hexagonal lattice (such as α-quartz). The hexagonal crystal family consists of the 12 point groups such that at least one of their space groups has the hexagonal lattice as underlying lattice, and is the union of the hexagonal crystal system and the trigonal ...