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In two-dimensional space there are 5 Bravais lattices, [5] grouped into four lattice systems, shown in the table below. Below each diagram is the Pearson symbol for that Bravais lattice. Note: In the unit cell diagrams in the following table the lattice points are depicted using black circles and the unit cells are depicted using parallelograms ...
For elements that are solid at standard temperature and pressure the first table gives the crystalline structure of the most thermodynamically stable form(s) in those conditions. Each element is shaded by a color representing its respective Bravais lattice, except that all orthorhombic lattices are grouped together.
The three dimensions of space afford 14 distinct Bravais lattices describing the translational symmetry. All crystalline materials recognized today, not including quasicrystals, fit in one of these arrangements. The fourteen three-dimensional lattices, classified by lattice system, are shown above.
In Hermann–Mauguin notation, space groups are named by a symbol combining the point group identifier with the uppercase letters describing the lattice type. Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions:
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.
The table below organizes the space groups of the monoclinic crystal system by crystal class. It lists the International Tables for Crystallography space group numbers, [ 2 ] followed by the crystal class name, its point group in Schoenflies notation , Hermann–Mauguin (international) notation , orbifold notation, and Coxeter notation, type ...
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 ...
Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c, which is different from a).