That is, if $P$ is a finite set, and $C$ is the set of points in $P$ which lie on the boundary of the convex hull of $P$, then is $P$ contained in the convex hull of $C$?

It seems true intuitively. Any help would be greatly appreciated.

That is, if $P$ is a finite set, and $C$ is the set of points in $P$ which lie on the boundary of the convex hull of $P$, then is $P$ contained in the convex hull of $C$?

It seems true intuitively. In my problem, it is okay to assume that $P\subset\mathbb{R}^d$. Any help would be greatly appreciated.

That is, if $C$ is the set of points in $P$ which lie on the boundary of the convex hull of $P$, then is $P$ contained in the convex hull of $C$?

It seems true intuitively. For my problem, assuming that $P$ is a finite set is okay. Any help would be greatly appreciated.

That is, if $P$ is a finite set, and $C$ is the set of points in $P$ which lie on the boundary of the convex hull of $P$, then is $P$ contained in the convex hull of $C$?

It seems true intuitively. Any help would be greatly appreciated.