The grain boundaries are the thin rings separating the grains, thicker annuli of hexagonal cells. Each dislocation introduces a new parastichy to maintain the density of points or cells as constant as possible. The underlying arithmetic of this concentric organization [@sadoc2] is that of Fibonacci numbers. It can be summarized as a sequence $c(s)$ of cell types {hexagon, pentagon, heptagon} along the generative spiral, that is an encoding of the structure to be discussed below [^3].

Incidentally, the terminology “spiral lattice” is well-chosen since the parastichies play the role of reticular lines in a classical 2D lattice. We call [*core*]{} the open disk of cells inside the innermost ring of defects.

Plane or curved phyllotaxis
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Phyllotaxis can be viewed as a succession of bent hexagonal grains connected by grain boundaries, outside an inner core. Bending is a shear stress that can be related to the curvature of the substrate. On the plane, using a Fermat spiral as generative spiral with a radial law demanding equi-sized cells, the foam is subjected to a (Poisson) shear stress, i.e. compressed radially and expanded azimuthally. By contrast, a hexagonal crystal wrapped with chirality on a cylinder has no shear stress. This wrapped hexagonal 