Centered Rectangular Lattice on:
[Wikipedia]
[Google]
[Amazon]
The rectangular lattice and rhombic lattice (or centered rectangular lattice) constitute two of the five two-dimensional Bravais lattice types. The
The primitive rectangular lattice can also be described by a centered rhombic unit cell, while the centered rectangular lattice can also be described by a primitive rhombic unit cell. Note that the length in the lower row is not the same as in the upper row. For the first column above, of the second row equals of the first row, and for the second column it equals .
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
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 lengths.
Bravais lattices
There are two rectangular Bravais lattices: primitive rectangular and centered rectangular (also rhombic).
The primitive rectangular lattice can also be described by a centered rhombic unit cell, while the centered rectangular lattice can also be described by a primitive rhombic unit cell. Note that the length in the lower row is not the same as in the upper row. For the first column above, of the second row equals of the first row, and for the second column it equals .
Crystal classes
The ''rectangular lattice'' class names, Schönflies notation, Hermann-Mauguin notation,orbifold notation
In geometry, orbifold notation (or orbifold signature) is a system, invented by the mathematician William Thurston and promoted by John Conway, for representing types of symmetry groups in two-dimensional spaces of constant curvature. The advanta ...
, Coxeter notation
In geometry, Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter group in a bracketed notation expressing the structure of a Coxeter-Dynkin diagram ...
, and wallpaper groups are listed in the table below.
References
{{Crystal systems Lattice points Crystal systems