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2. Bravais lattice - Wikipedia

   en.wikipedia.org/wiki/Bravais_lattice

   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

3. List of planar symmetry groups - Wikipedia

   en.wikipedia.org/wiki/List_of_planar_symmetry_groups

   The 17 wallpaper groups, with finite fundamental domains, are given by International notation, orbifold notation, and Coxeter notation, classified by the 5 Bravais lattices in the plane: square, oblique (parallelogrammatic), hexagonal (equilateral triangular), rectangular (centered rhombic), and rhombic (centered rectangular).

4. Crystal system - Wikipedia

   en.wikipedia.org/wiki/Crystal_system

   These lattices are classified by the space group of the lattice itself, viewed as a collection of points; there are 14 Bravais lattices in three dimensions; each belongs to one lattice system only. They [ clarification needed ] represent the maximum symmetry a structure with the given translational symmetry can have.

5. Crystal structure - Wikipedia

   en.wikipedia.org/wiki/Crystal_structure

   The geometry of the unit cell is defined as a parallelepiped, providing six lattice parameters taken as the lengths of the cell edges (a, b, c) and the angles between them (α, β, γ). The positions of particles inside the unit cell are described by the fractional coordinates ( x i , y i , z i ) along the cell edges, measured from a reference ...

6. 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 ...

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8. Rectangular lattice - Wikipedia

   en.wikipedia.org/wiki/Rectangular_lattice

   The rectangular lattice and rhombic lattice (or centered rectangular lattice) constitute two of the five two-dimensional Bravais lattice types. [1] The symmetry categories of these lattices are wallpaper groups pmm and cmm respectively. The conventional translation vectors of the rectangular lattices form an angle of 90° and are of unequal ...

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