We know that every point in a polytope is either a vertex or can be represented by a convex combination of vertices.
But my question is: are there polytopes in $\mathbb{R}^{m}$ such that every point can be represented with fewer than $m$ vertices. Better yet, on the order of $O(\sqrt{m})$ vertices, and ideally less than or equal to $\sqrt{m}$ vertces
Do such polytopes/polyhedra have name, or any other refernces on the smallest number of vertices needed to represent a point inside a polyhedron will be appreciated!