cells). Going down (or inwards in Fig.\[fg2\]), a circular ring of defects constitutes a grain boundary, a complete layer of $f_{i+1}$ cells that are truncated squares, namely $f_{i-1}$ heptagons, $f_{i-2}$ topological hexagons and $f_{i-1}$ pentagons, successively along the $f_{i}$ turns of the generative spiral.

Layers are defined going down (inwards) from each grain boundary. The innermost layer of each grain may be incomplete. Notably, in the core (from the innermost ring of defect), one denotes the first layer $\mu = 1$ within parentheses () in the sequence $c(s) = (, , ,), \dots$ of cells along the generative spiral, characterized by their edge numbers.

Figure \[newfig\] gives the innermost layers of the planar phyllotactic structure of Fig.2, defined inwards from the innermost defect ring, the twenty-one cells $s =10 - 30$ constituting layer 3 (open circles)

In spherical phyllotaxis, for $n=43-75$, the polar circle $[6,6,6,6,6,6,6,6,5,5,5,5,5]$ constitutes layer $\mu = 2$, going inwards, with the five pentagons $s=12-16$ as defect inclusions. Layer $\mu = 1$ ($(5,6,6)$) has the three cells $s=1,2,3$, whether going inwards or outwards. But, going outwards, layer $\mu=2$ has only eight cells, the five pentagons of the polar circle joining with the first eight hexagons of grain $ 