MathDB
convex hull

Source: miklos schweitzer 1992 q9

October 25, 2021
combinatorial geometryeuclidean geometryconvex geometry

Problem Statement

Let K be a bounded, d-dimensional convex polyhedron that is not simplex and P is a point on K. Show that if vertices P1,...,PkP_1 , ..., P_k are not all on the same face of K, then one of them can be omitted so that the convex hull of the remaining vertices of K still contains P.
caratheodory's theorem might be useful.