  A classical result of Namioka and Phelps states that the square is a test
object to verify semi-simplexity in the tensor theory of convex compact sets.
By using the quantization of generalized Namioka-Phelps test spaces we
formulate a nuclearity criteria for C*-algebras, which establishes a
non-commutative version of their result. The proof we suggest covers the
nuclearity characterization via non-commutative polyhedron outlined by Effros.
Several matrix systems studied by Farenick and Paulsen are shown to be test
systems for nuclearity. We also prove that the standard Namioka-Phelps test
space is C*-nuclear. We propose a partition of unity property for C*-algebras
which distinguishes nuclear C*-algebras among the others.
