Editing Crystal structure (section)

==== Cubic structures ====
For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length (usually denoted ''a''); similarly for the reciprocal lattice. So, in this common case, the Miller indices (''ℓmn'') and [''ℓmn''] both simply denote normals/directions in [[Cartesian coordinates]]. For cubic crystals with [[lattice constant]] ''a'', the spacing ''d'' between adjacent (ℓmn) lattice planes is (from above):
:<math>d_{\ell mn}= \frac {a} { \sqrt{\ell ^2 + m^2 + n^2} }</math>
Because of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and have equivalent directions and planes:

*Coordinates in ''angle brackets'' such as {{angbr|100}} denote a ''family'' of directions that are equivalent due to symmetry operations, such as [100], [010], [001] or the negative of any of those directions.
*Coordinates in ''curly brackets'' or ''braces'' such as {100} denote a family of plane normals that are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.

For [[face-centered cubic]] (fcc) and [[body-centered cubic]] (bcc) lattices, the primitive lattice vectors are not orthogonal. However, in these cases the Miller indices are conventionally defined relative to the lattice vectors of the cubic [[supercell (crystal)|supercell]] and hence are again simply the [[Cartesian coordinates|Cartesian directions]].