{{Short description|2-dimensional lattice}} {| class=wikitable align=right |+ Rectangular lattices |150px |150px |- !Primitive !Centered |- |150px |150px |- !pmm !cmm |}

The '''rectangular lattice''' and '''centered rectangular lattice''' (or rhombic lattice) constitute two of the five two-dimensional Bravais lattice types.<ref name=":0">{{Cite web|last=Rana|first=Farhan|title=Lattices in 1D, 2D, and 3D|url=https://courses.cit.cornell.edu/ece407/Lectures/handout4.pdf|url-status=live|archive-url=https://web.archive.org/web/20201218214110/https://courses.cit.cornell.edu/ece407/Lectures/handout4.pdf|archive-date=2020-12-18|website=Cornell University}}</ref> 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 lengths. {{clear}}

== Bravais lattices == There are two rectangular Bravais lattices: primitive rectangular and centered rectangular (or rhombic).

thumb|right|300px|Rectangular vs rhombic unit cells for the 2D rectangular lattices.

{| class=wikitable ! Bravais lattice ! Rectangular ! Centered rectangular |- align=center ! Pearson symbol | op | oc |- ! Standard unit cell | 100px | 100px |- ! Rhombic unit cell | 100px<!-- Do not switch the images. In the rhombic axis setting, the primitive and centered lattices swap in centering type. --> | 100px<!-- Do not switch the images. In the rhombic axis setting, the primitive and centered lattices swap in centering type. --> |}

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 <math>a</math> in the lower row is not the same as in the upper row. For the first column above, <math>a</math> of the second row equals <math>\sqrt{a^2+b^2}</math> of the first row, and for the second column it equals <math>\frac{1}{2} \sqrt{a^2+b^2}</math>.

== Crystal classes == The ''rectangular lattice'' class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below. {| class="wikitable" |- ! colspan=4|Geometric class, point group ! rowspan=2|Arithmetic <br/>class ! rowspan=2 colspan=2|Wallpaper groups |- align=center !Schön. ||Intl ||Orb. ||Cox. |- align=center |rowspan=2| D<sub>1</sub>||rowspan=2|m||rowspan=2|(*)||rowspan=2|[&nbsp;] | Along | pm<BR>(**) | pg<BR>(××) |- align=center | Between | cm<BR>(*×) |&nbsp; |- align=center |rowspan=2|D<sub>2</sub>||rowspan=2|2mm||rowspan=2|(*22)||rowspan=2|[2] | Along | pmm<BR>(*2222) | pmg<BR>(22*) |- align=center | Between | cmm<BR>(2*22) | pgg<BR>(22×) |}

== References == {{reflist}}

{{Crystal systems}}

Category:Lattice points Category:Crystal systems

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