rectangular lattice

class=wikitable align=right \|+ Rectangular lattices \|150px \|150px
Primitive !Centered
150px \|150px
pmm !cmm

class=wikitable align=right

|+ Rectangular lattices

|150px

Primitive

!Centered

150px

|150px

pmm

!cmm

The rectangular lattice and rhombic lattice (or centered rectangular lattice) constitute two of the five two-dimensional Bravais lattice types.{{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}} 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.

Bravais lattices

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

File:Rectangular unit cells.svg

class=wikitable ! Bravais lattice ! Rectangular ! Centered rectangular
align=center ! Pearson symbol \| op \| oc
Standard unit cell \| 100px \| 100px
Rhombic unit cell \| 100px \| 100px

class=wikitable

! Bravais lattice

! Rectangular

! Centered rectangular

align=center

! Pearson symbol

| op

| oc

Standard unit cell

| 100px

Rhombic unit cell

| 100px

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

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.

colspan=4\|Geometric class, point group ! rowspan=2\|Arithmetic class ! rowspan=2 colspan=2\|Wallpaper groups
class="wikitable"
align=center !Schön.	Intl	Orb.	Cox.
align=center \|rowspan=2\| D₁	rowspan=2\|m	rowspan=2\|(*)	rowspan=2\|[ ] \| Along \| pm (**) \| pg (××)
align=center \| Between \| cm (*×) \|
align=center \|rowspan=2\|D₂	rowspan=2\|2mm	rowspan=2\|(*22)	rowspan=2\|[2] \| Along \| pmm (2222) \| pmg (22)
align=center \| Between \| cmm (2*22) \| pgg (22×)

References

Category:Lattice points

Category:Crystal systems

colspan=4\|Geometric class, point group ! rowspan=2\|Arithmetic class ! rowspan=2 colspan=2\|Wallpaper groups
class="wikitable"
align=center !Schön.	Intl	Orb.	Cox.
align=center \|rowspan=2\| D₁	rowspan=2\|m	rowspan=2\|(*)	rowspan=2\|[ ] \| Along \| pm (**) \| pg (××)
align=center \| Between \| cm (*×) \|
align=center \|rowspan=2\|D₂	rowspan=2\|2mm	rowspan=2\|(*22)	rowspan=2\|[2] \| Along \| pmm (2222) \| pmg (22)
align=center \| Between \| cmm (2*22) \| pgg (22×)