  Let A be a unital separable simple infinite-dimensional nuclear C*-algebra
with at least one tracial state. We prove that if the trace space of A has
compact finite-dimensional extreme boundary then there exist unital embeddings
of matrix algebras into a certain central sequence algebra of A which is
determined by the uniform topology on the trace space. As an application, it is
shown that if furthermore A has strict comparison then A absorbs the Jiang-Su
algebra tensorially.
