Given a set $S_n$ of $n$ points $\mathbf{x}_1, \mathbf{x}_2, \ldots, \mathbf{x}_n\in\mathbb{R}^d$, such that every $(d+1)$-tuple in $S_n$ is affinely independent, and let $C(S_n)$ be the convex hull of the points of $S$. Let now $T(S_n)$ be the set of all triplets $\{\mathbf{x}_i, \mathbf{x}_j, \mathbf{x}_k\}$ of points in $S_n$ for all $1\le i<j<k\le n$ such that no point of each triangle having $\mathbf{x}_i, \mathbf{x}_j, \mathbf{x}_k$ as vertices, is an interior point of $C(S_n)$.
Question: What is the maximum cardinality $m(n,d)$ of $T$ over all possible sets $S_n$ of $n$ points in $\mathbb{R}^d$?