[@GLICK20111019; @Gekhtman2016; @fock2014loop]. Most works on the the pentagram map regard it as a dynamical system on the space of polygons modulo projective equivalence. And indeed that is the setting where most remarkable features of that map such as integrability reveal themselves. That said, the pentagram map on actual [polygons]{} (as opposed to projective equivalence classes) also has interesting geometry. One of the early results in this direction was Schwartz’s proof of the exponential convergence of successive images of a convex polygon under the pentagram map to a point (see Figure \[Fig2\]). That limit point is a natural invariant of a polygon and can be thought of as a projectively natural version of the center of mass. However, it is not clear a priori whether this limit point can be expressed in terms of coordinates of the vertices by any kind of an explicit formula. A remarkable recent result by M.Glick [@glick2020limit] is that this dependence is in fact algebraic. Moreover, there exists an operator in ${\mathbb R}^3$ whose matrix entries are rational in terms of polygon’s vertices, while the coordinates of the limit point are given by an eigenvector of that operator. Therefore, coordinates of the limit point can 