Reversible electronic energy transfer (homo-FRET) in cyclic multichromophoric systems is studied for sets of n identical fluorophores arranged in regular polygons (triangle, square, pentagon, etc.). A general analytic expression for the anisotropy decay is obtained for a regular polygon of any order, under the assumptions of isotropic interaction and nearest-neighbor FRET. A graphical way of connecting the decay form and polygon geometry based on the Frost circle is also presented. The consequences of the relaxation of these assumptions on the anisotropy decay are also discussed and analyzed in detail for the heptagon.