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  2. 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 ...

  3. Brillouin zone - Wikipedia

    en.wikipedia.org/wiki/Brillouin_zone

    The reciprocal lattices (dots) and corresponding first Brillouin zones of (a) square lattice and (b) hexagonal lattice. In mathematics and solid state physics, the first Brillouin zone (named after Léon Brillouin) is a uniquely defined primitive cell in reciprocal space.

  4. 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 ...

  5. Miller index - Wikipedia

    en.wikipedia.org/wiki/Miller_index

    This is based on the fact that a reciprocal lattice vector (the vector indicating a reciprocal lattice point from the reciprocal lattice origin) is the wavevector of a plane wave in the Fourier series of a spatial function (e.g., electronic density function) which periodicity follows the original Bravais lattice, so wavefronts of the plane wave ...

  6. Crystal structure - Wikipedia

    en.wikipedia.org/wiki/Crystal_structure

    Of the 32 point groups that exist in three dimensions, most are assigned to only one lattice system, in which case the crystal system and lattice system both have the same name. However, five point groups are assigned to two lattice systems, rhombohedral and hexagonal, because both lattice systems exhibit threefold rotational symmetry.

  7. List of space groups - Wikipedia

    en.wikipedia.org/wiki/List_of_space_groups

    The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2 1 is a 180° (twofold) rotation followed by a translation of ⁠ 1 / 2 ⁠ of the lattice vector. 3 1 is a 120° (threefold) rotation followed by a translation of ⁠ 1 / 3 ⁠ of ...

  8. File:Honeycomb lattice - hexagonal lattice with a two-atom ...

    en.wikipedia.org/wiki/File:Honeycomb_lattice...

    English: Honeycomb lattice is not a Bravais lattice, but can be considered a hexagonal Bravais lattice with a two-atom basis (atoms A and B). Vectors a₁ and a₂ are primitive translation vectors. Vectors a₁ and a₂ are primitive translation vectors.

  9. Close-packing of equal spheres - Wikipedia

    en.wikipedia.org/wiki/Close-packing_of_equal_spheres

    Both arrangements produce a face-centered cubic lattice – with different orientation to the ground. Hexagonal close-packing would result in a six-sided pyramid with a hexagonal base. Collections of snowballs arranged in pyramid shape. The front pyramid is hexagonal close-packed and rear is face-centered cubic.