We present a general method for constructing extensional models for the Girard-Reynolds polymorphic lambda calculus - the polymorphic extensional collapse. The method yields models that satisfy additional, computationally motivated constraints like having only two polymorphic booleans and having only the numerals as polymorphic integers. Moreover, the method can be used to show that any simply typed lambda model can be fully and faithfully embedded into a model of the polymorphic lambda calculus.