of the projective group ${{\mathbb P}\mathrm{GL}}({\mathbb P}^2)$, i.e. a linear operator on ${\mathbb R}^3$ defined up to adding a scalar matrix. The following is our main result.

\[thm1\] The infinitesimal monodromy of a closed polygon $P$ coincides with Glick’s operator $G_P$, up to addition of a scalar matrix.

This result provides another perspective on the limit point. Namely, observe that for $z \approx 1$ the monodromy $M_z$ of the deformed polygon is given by $$M_z \approx I + (z-1)(G_P + \lambda I),$$ up to higher order terms. Thus, the eigenvectors of $G_P$, and in particular the limit point, coincide with limiting positions of eigenvectors of $M_z$ as $z \to 1$. At least one of the eigenvectors of $M_z$ has a geometric meaning. Namely, the deformed polygon $P(z)$ can be thought of as a spiral, and the center of that spiral must be an eigenvector of the monodromy. We believe that as $z \to 1$ that eigenvector converges to the limiting point of the pentagram map (and not to one of the two other eigenvectors). If this is true, then we have the following picture. The scaling symmetry turns a closed polygon into a spiral. As the scaling parameter $z$ goes 