Abstract: β-helix proteins contain a solenoid domain of parallel β-strands folded into a large prism. Each turn of the solenoid, called a β-coil, consists of a succession of a few (usually three) β-strands. β-strands from adjacent coils stack to form parallel β-sheets that make up the faces of the prism. These faces are linked by loop regions that protrude from the helix and, in many cases, form the binding site of the helix. The cross section of this prism is typically L-shaped in right-handed parallel β-helices and triangular in left-handed parallel β-helices. Left-handed and right-handed β-helices have a different cross section The stability of the domain is mainly obtained by the stacking of similar residue side-chains at equivalent positions in successive coils, both inside and outside the helix. The inward side chains are mainly hydrophobic and, when not, maximal hydrogen bonding or electrostatic interactions neutralise their polar or charged groups. We have formalised the intuitive notion of a β-helix in a set of objective algorithms that recognize automatically the basic structural elements of β-helices: residue stacks, β-coils, cores and β-helices. We define the core of a β-helix as the helical domain of the protein, as distinguished from the protruding loop regions.