They can be defined in two ways: The hydrogen bond criterion is the one most appropriate for everyday use, partly because it gives rise to four distinct categories; the distance criterion gives rise to the same four categories but yields additional turn types.
The hydrogen bond criterion for beta turns, applied to polypeptides whose amino acids are linked by trans peptide bonds, gives rise to just four categories, as shown by Venkatachalam in 1968.
Type II beta turns, on the other hand, often occur in association with beta-sheet as part of beta-links.
The four types of beta turn are distinguished by the φ, ψ angles of residues i+1 and i+2 as shown in the table below giving the typical average values.
Glycines are especially common as amino acids with positive φ angles; for prolines such a conformation is sterically impossible but they occur frequently at amino acid positions where φ is negative.