Basic Maths for Protein Crystallographers
	Lattice geometry

Diffraction from a crystal lattice is visible at discrete points conveniently indexed as an integer triple (h,k,l), or in vector notation as ha^*+kb^*+lc^*, relative to the reciprocal lattice vectors a^*,b^*,c^*. These are defined to have the properties

a*· a = b*· b = c*· c = 1

a*· b = a*· c = b*· c = 0

i.e. a^* is perpendicular to b and c, and therefore parallel to b×c. E.g. in P3₁:

where c and c^* lie vertically in the plane of the drawing, and a^* comes perpendicularly out of the plane of the drawing.