Editing Bravais lattice (section)

==In 2 dimensions==
{{further|Lattice (group)}}
In two-dimensional space there are 5 Bravais lattices,<ref>{{cite book |last=Kittel |first=Charles |title=[[Introduction to Solid State Physics]] |orig-year=1953 |chapter-url= http://www.wiley.com/WileyCDA/WileyTitle/productCd-047141526X.html |access-date=2008-04-21 |edition=Seventh  |year=1996 |publisher=John Wiley & Sons |location=New York  |isbn=978-0-471-11181-8 |pages=10 |chapter=Chapter 1}}</ref> grouped into four [[lattice system]]s, 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 (which may be squares or rectangles) outlined in black. Although each of the four corners of each parallelogram connects to a lattice point, only one of the four lattice points technically belongs to a given unit cell and each of the other three lattice points belongs to one of the adjacent unit cells. This can be seen by imagining moving the unit cell parallelogram slightly left and slightly down while leaving all the black circles of the lattice points fixed.

{| class="wikitable skin-invert-image"
! rowspan=2| Lattice system
! rowspan=2| Point group <br />([[Schoenflies notation|Schönflies notation]])
! colspan=2| 5 Bravais lattices
|-
! Primitive (p)
! Centered (c)
|- align=center
! Monoclinic (m)
| C<sub>2</sub>
| [[File:2d mp.svg|90px|Oblique]]<br/>[[Oblique lattice|Oblique]]<br/>(mp)
|
|- align=center
! Orthorhombic (o)
| D<sub>2</sub>
| [[File:2d op rectangular.svg|110px|Oblique]]<br/>[[Rectangular lattice|Rectangular]]<br/>(op)
| [[File:2d oc rectangular.svg|110px|Oblique]]<br/>Centered rectangular <br/>(oc)
|- align=center
! Tetragonal (t)
| D<sub>4</sub>
| [[File:2d tp.svg|90px|Oblique]]<br/>[[Square lattice|Square]]<br/>(tp)
|
|- align=center
! Hexagonal (h)
| D<sub>6</sub>
| [[File:2d hp.svg|100px|Oblique]]<br/>[[Hexagonal lattice|Hexagonal]]<br/>(hp)
|
|}
{{Clear}}

The unit cells are specified according to the relative lengths of the cell edges (''a'' and ''b'') and the angle between them (''θ''). The area of the unit cell can be calculated by evaluating the [[Vector norm|norm]] {{nowrap|{{norm|'''a''' × '''b'''}}}}, where '''a''' and '''b''' are the lattice vectors. The properties of the lattice systems are given below:

{| class=wikitable
! Lattice system
! Area
! Axial distances (edge lengths)
! Axial angle
|-
! Monoclinic
| <math>ab \, \sin\theta</math>
| 
| 
|-
! Orthorhombic
| <math> ab </math>
| 
| ''θ'' = 90°
|-
! Tetragonal
| <math>a^2</math>
| ''a'' = ''b''
| ''θ'' = 90° 
|-
! Hexagonal
|<math>\frac{\sqrt{3}}{2}\, a^2</math>
| ''a'' = ''b''
| ''θ'' = 120°
|}
{{Clear}}