Based on the previous work (Li P, Deng W J 2009 Acta Phys. Sin. 58 02713), the quantum transportation of electron through arbitrary equilateral polygons quantum rings with Rashba spin-orbit interaction is studied. With the typical method of quantum network and the Landauer-Büttiker formalism, we analytically solve the scattering problem of electron through equilateral polygonal quantum ring, and obtain the relevant formula for spin transportation conductance. The characteristics of the conductance varying with the wave-vector of electron, the strength of spin-orbit interaction, the number of polygon edges, and the ways of leads connecting to quantum rings are discussed. In the limit of infinite number of edges of polygon, we prove that the formula is consistent with the results obtained directly from the circular model of quantum rings.