four incident on a vertex which is a critical point of a $T1$ (a natural four-corner boundary, with the two main parastichies crossing at right angle [@coxeter]). The squares are slightly truncated to specify the number of sides of the neighboring cells, and it is the truncation mode that flips ($T1$) under shear or growth. The hexagonal cells constituting a grain lie between the pentagons of one grain boundary and the heptagons of the next boundary.

The grain boundary in phyllotaxis is a circular ring of defects, the cells are squares, slightly truncated, and the main parastichies cross perpendicularly, so that the grain boundary can be represented as a strip in a square lattice, with the thin diagonal lines identified (Fig.\[fg4\]a). The strip is mapped into a circular ring of defects (non-hexagonal cells) of Fig. 2. The mapping is conformal (it conserves the angles), so that the orthogonality of the main parastichies and the square shape of the cells are conserved.

In planar and spherical phyllotaxis, the innermost ring of defects contains five more pentagons (of topological charge $+1$) than heptagons (topological charge $-1$) [@miri]. This is because the topological charge of a disk (flattened hemisphere) must be $+6$, with 