 Carathéodory conjecture

The Carathéodory conjecture is a mathematical conjecture in the field of geometry that deals with the concept of convex polygons in three-dimensional space. Specifically, the conjecture states that for any simple closed convex surface in three-dimensional Euclidean space, the surface can be covered by at most five planes. This conjecture was proposed by the Greek mathematician Constantin Carathéodory in 1911.