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We describe the configuration space $\mathbf{S}$ of polygons with prescribededge slopes, and study the perimeter $\mathcal{P}$ as a Morse function on$\mathbf{S}$. We characterize critical points of $\mathcal{P}$ (these are\textit{tangential} polygons) and compute their Morse indices. This setup ismotivated by a number of results about critical points and Morse indices of theoriented area function defined on the configuration space of polygons withprescribed edge lengths (flexible polygons). As a by-product, we present anindependent computation of the Morse index of the area function (obtainedearlier by G. Panina and A. Zhukova).

Polygons with prescribed edge slopes: configuration space and extremal points of perimeter