Question about lower convex hull of a polytope.
Consider the pyramid with triangular $black$ face as the base of the pyramid.
This is a polytope constructed of $4$ coordinate points ($3$ at the plane and one at the top) in $\mathbb{R}^3$.
My question:
What would be the lower convex hull of the pyramid (polytope)?
We know that a convex is divided into two parts, lower convex hull and upper convex hull.
From here, we get the lower convex hull is formed by those vertices whose upward ray doesn't intersect the convex hull.
So this shows that in case of pyramid shown above, only the $3$ points in the plane contribute the lower convex hull which is just the $black$ face attached with the ground, because upward rays from these $3$ points don't intersect the pyramid.
Am I right about that ?