1) The document generalizes Lami's Theorem, which relates the magnitudes of three coplanar, concurrent and non-collinear forces in static equilibrium, to systems with any odd number of forces. 2) It shows that for cyclic polygons with an odd number of sides, the sine rule relating side lengths and opposite interior angles takes the same form as Lami's Theorem. 3) The paper also describes how to transform n-gons into vector diagrams and vice versa, and derives a condition for when a vector diagram can represent a cyclic polygon.