About collagen, a tribute to Yves Bouligand.

Yves Bouligand's analysis of the organizations of biological materials in relation to those of liquid crystals enabled the development of the idea that physical forces exerting their actions under strong spatial constraints determine the structures and morphologies of these materials. The different levels of organization in collagen have preoccupied him for a long time. We present here our recent works in this domain that we were still discussing with him a few months before his death at the age of 76 on 21 January 2011. After recalling the hierarchical set of structures built by collagen molecules, we analyse them, exploiting the properties of the curved space of the hypersphere and of the algorithm of phyllotaxis. Those two geometrical concepts can be proposed as structural archetypes founding the polymorphism of this complex material of biological origin.