This volume is a monograph on the geometric structure of a certain class of ("comprehensive") compact polyhedra called Cephoids. A Cephoid is a Minkowski sum of finitely many standardized simplices. The emphasis rests on the Pareto surface of Cephoids which consists of certain translates of simplices, algebraic sums of subsimplices etc. Cephoids appear in Operations Research (Optimization), in Mathematical Economics (Free Trade theory), and in Cooperative Game Theory. In particular, in the context of Cooperative Game Theory the notions of a Cephoid serves to construct "solutions" or "values" for bargaining problems and non-side payment games.