crystal can be conformally mapped on a plane to yield a phyllotaxis that is a conformal (single) crystal with only hexagonal cells (outside a central core) and zero shear strain [@rothen]. The sizes of the florets increase radially outwards and the generative spiral is the equiangular spiral $\rho \sim \exp{\theta}$ (Bernoulli). The curvature of the substrate, the nature of the generative spiral and the sizes of the cells are therefore intertwined properties of the phyllotactic structure.

A grain is denoted as $(f_{i-1},f_{i-2},f_{i-3})$ (i.e. hexagonal cells in phyllotaxis $(f_{i-1},f_{i-2},f_{i-3})$) and encoded as $...,6,6,6,...$ in the sequence $c(s)$. Spherical phyllotaxis [^4] is obtained by the mapping of points on a finite cylinder tangent at the equator to the sphere with the same radius $R$ and height $2R$. The finite cylinder and the sphere have the same area $4\pi R^2$. Points on the cylinder are located on a regular helix defined by $\theta= (2 \pi/\tau) s$ and a constant pitch $h$ related to the number of points on the sphere. They constitute a perfect lattice without defects wrapped on the cylinder, with a constant density of points. Generically, a point $s$ has six neighbors at positions $s\pm\delta s$ with the $\delta s$ equal 