Helices and dense packing. of spherical objects are two closely related pro
blems. For instance, the Boerdijk-Coxeter helix, which is obtained as a lin
ear packing of regular tetrahedra, is a very efficient solution to some clo
se-packing problems. The shapes of biological helices result from various k
inds of interaction forces, including steric repulsion. Thus, the search fo
r a maximum density can lead to structures related to thf Boerdijk-Coxeter
helix. Examples are presented for the alpha-helix structure in proteins and
for the structure of the protein collagen, but there are other examples of
helical packings at different scales in biology. Models based on packing e
fficiency related to the Boerdijk-Coxeter helix, explain, mainly from topol
ogical arguments, why the number of amino acids per turn is close to 3.6 in
alpha-helices and 2.7 in collagen.