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Phyllotaxis, the search for the most homogeneous and dense organizations ofsmall disks inside a large circular domain, was first developed to analyzearrangements of leaves or florets in plants. Then it has become an object ofstudy not only in botany, but also in mathematics, computer simulations andphysics. Although the mathematical solution is now well known, an algorithmsetting out the centers of the small disks on a Fermat spiral, the very natureof this organization and its properties of symmetry remain to be examined. Thepurpose of this paper is to describe a phyllotactic organization of pointsthrough its Voronoi cells and Delaunay triangulation and to refer to theconcept of defects developed in condensed matter physics. The topologicalconstraint of circular symmetry introduces an original inflation-deflationsymmetry taking the place of the translational and rotational symmetries ofclassical crystallography.

Phyllotaxis: a non conventional crystalline solution to packing efficiency in situations with radial symmetry