  Phyllotaxis, the search for the most homogeneous and dense organizations of
small disks inside a large circular domain, was first developed to analyze
arrangements of leaves or florets in plants. Then it has become an object of
study not only in botany, but also in mathematics, computer simulations and
physics. Although the mathematical solution is now well known, an algorithm
setting out the centers of the small disks on a Fermat spiral, the very nature
of this organization and its properties of symmetry remain to be examined. The
purpose of this paper is to describe a phyllotactic organization of points
through its Voronoi cells and Delaunay triangulation and to refer to the
concept of defects developed in condensed matter physics. The topological
constraint of circular symmetry introduces an original inflation-deflation
symmetry taking the place of the translational and rotational symmetries of
classical crystallography.
