projective geometry, whose full significance is yet to be understood.

In the present paper we show that Glick’s operator $G_P$ can be interpreted as *infinitesimal monodromy*. To define the latter, consider the space of *twisted polygons*, that are polygons closed up to a projective transformation, known as the *monodromy*. Any closed polygon can be viewed as a twisted one, with trivial monodromy. To define the infinitesimal monodromy we deform a closed polygon into a genuine twisted one. To construct such a deformation, we use what is known as the *scaling symmetry*. The scaling symmetry is a $1$-parametric group of transformations of twisted polygons which commutes with the pentagram map. That symmetry was instrumental for the proof of complete integrability of the pentagram map [@ovsienko2010pentagram].

Applying the scaling symmetry to a given closed polygon $P$ we get a family $P_z$ of polygons depending on a real parameter $z$ and such that $P_1 = P$. Thus, the monodromy $M_z$ of $P_z$ is a projective transformation depending on $z$ which is the identity for $z = 1$. By definition, the infinitesimal monodromy of $P$ is the derivative $dM_z/dz$ at $z = 1$. This makes the infinitesimal monodromy an element of the Lie algebra 