Did Plato Solve the Problem of How to Translate Theory into Practice in his “Republic”?

My idea is to (i) sketch the basic assumption upon which rests or seems to rest Plato's theory of how to construct the ideal city-state before (ii) letting him put forth arguments against the possibility of constructing such a state on the basis of purely theoretical presuppositions, and (iii) then questioning what seems to have been his basic premisses. My aim is to show that there is ample evidence in Plato's text that he realizes that the problem of how to translate theory into practice cannot be solved theoretically, i.e. the project of constructing the empirically ideal city-state cannot be implemented.