Fix a triangulation of a (flat) n-gon and consider all spatial n-gons in the 3-dimensional Euclidean space with the fixed integer side lengths $l_1,\ldots,l_n$ and (arbitrary) integer lengths of the diagonals forming the given triangulation, modulo isometries of the Euclidean space. It turns out that the set of all such spatial polygons is a disjoint union of tori, with the number of the connected components depending on the integers $l_i$ -- but not on the triangulation. I will explain how to make this statement obvious using the Representation Theory of SL(2). I will also discuss some Combinatorics standing behind this fact.