It is shown that the coloured isomorphism class of a unital, simple, Z-stable, separable amenable C * -algebra satisfying the Universal Coefficient Theorem (UCT) is determined by its tracial simplex. n k=1 u k ΟΟ(a)u * k = a and n k=1 v k ΟΟ(b)v * k = b for all a β A and all b β B.The present notion, coloured isomorphism, on the other hand, has order zero maps at the level of ultrapowers A Ο and B Ο (and so includes the case that the ultrapower maps are induced by a sequence of order zero maps at the level