to three successive Fibonacci numbers depending on the pitch of the helix drawn on the cylinder. The Voronoi cells are then all hexagons with equal area. For particular values of the pitch, the Voronoi cells are squares and the tessellation by squares has non-generic four-corner boundaries with degree $z = 4$ (the critical point of a $T1$ transformation) [@coxeter],[@koch1].

The points on the cylinder are mapped on the sphere orthogonally to the polar axis so that the area per point on the sphere is the same as on the cylinder (the area of a zone between two parallel planes is the same on a sphere of radius $R$ and on the tangent cylinder orthogonal to the planes). But such a projection on the sphere, even if it conserves the area of the Voronoi cells and the pitch of the helix, introduces inhomogeneous shear in the structure. This shearing, at constant area, is given by a compression factor $\sin(\phi)$ changing the length of the equator into that of a parallel (at $\phi$), and an expansion factor along meridians. Shear can change the incidence relations between neighbors so that first neighbors are not necessarily the same as on the crystalline cylinder and 