Simplex of states in a $C^*$- algebra

Question

Let $A$ be a unital $C^*$- algebra. What does it mean by a simplex in the space of states on a $C^*$- algebra. I know that the space $S(A)$ of all states is a compact convex set in weak * topology induced from $A^*$. By definition, $n$- simplex is the convex hull of $n+1$ points. Can I use the same definition here in $S(A)$? Since $S(A)$ is convex, it makes sense. Or is there any extra conditions to be noted? Also what is a closed face in this simplex of states? Is it a normal simplex closed in the weak-* topology?