of an elementary topological transformation (whether a $T1$ or the disappearance of a cell) on the sequence $c(s)$ of cells $s=1,2,...$ along the generative spiral. We shall see that the phyllotactic structure (grain boundaries and organization into parastichies) is invariant under disappearance of the first cell $s=1$ of the sequence and suitable $T1$.

Disappearance of the first cell $s=1$
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The first cell $s=1$ is a pentagon, with five neighbors $s = (2,3,6,9,4)$, in cyclic order (see Fig.1b), marking the onset of the parastichies $1,2,5,8,3$, that are the first Fibonacci numbers characteristic of phyllotaxis [^5]. What happens if cell $s=1$ of the tessellation disappears ($o$)? One sees ([@dubertret] or Fig.1b), e.g. by removing the boundary between cells $1$ and $4$, that cells $2$ et $9$ lose a side ($-$) and cell $4$, filling the space left vacant by $1$, gains a side ($+$). All the other cells are topologically unchanged ($.$). Thus, disappearance of $s=1$ affects the sequence $c(s)$ of cells along the generative spiral through the operator ${\bf D} = (o,-,.,+,.,.,.,.,-,.,...)$ and the first cell is now $s=2$. The sequence $[(5,6,6),5,5,5,5,5],6,6,6\ldots$ is [*invariant*]{} under disappearance of $s=1$. Similarly, the sequence $(5,6,6),[(6,6,6,6,6),(6,6,6),(5,5,5,5,5)],6,6,\ldots$ (spheres $n=43-75$), invariant under disappearance of $1$, with 