Before revision:  We show that stable three-sided  matchings always exist, and present the PhD algorithm , a three-sided matching algorithm with polynomial running time which uses any two-sided stable matching algorithm as matching engine.
After revision:  We show that stable three-sided matchings always exist, and present an algorithm that, in time quadratic in the market size (up to log factors), finds a three-sided matching algorithm with polynomial running time which uses any two-sided stable matching algorithm as matching engine.