Editing Reciprocal lattice (section)

===Simple hexagonal lattice===

The reciprocal to a simple hexagonal Bravais lattice with [[lattice constants]] <math display="inline"> a</math> and <math display="inline"> c</math> is another simple hexagonal lattice with lattice constants <math display="inline"> 2\pi/c</math> and <math display="inline"> 4\pi/(a\sqrt3)</math> rotated through 90° about the ''c'' axis with respect to the direct lattice. The simple hexagonal lattice is therefore said to be self-dual, having the same symmetry in reciprocal space as in real space. Primitive translation vectors for this simple hexagonal Bravais lattice vectors are
<math display="block">
\begin{align}
a_1 & = \frac{\sqrt{3}}{2} a \hat{x} + \frac{1}{2} a \hat{y}, \\[8pt]
a_2 & = - \frac{\sqrt{3}}{2} a \hat{x} + \frac{1}{2}a\hat{y}, \\[8pt]
a_3 & = c \hat{z}.
\end{align} </math><ref>{{Cite book|last=Kittel|first=Charles | title=Introduction to Solid State Physics | publisher=John Wiley & Sons, Inc | year=2005 | isbn=0-471-41526-X | edition=8th | pages=44}}</ref>