MathDB
maximal no of edges a plane intersects a polyhedron having 100 edges.

Source: TOT 357 1992 Autumn O S6 - Tournament of Towns

June 10, 2024
combinatoricsgeometry3D geometrycombinatorial geometry

Problem Statement

Consider a polyhedron having 100100 edges.
(a) Find the maximal possible number of its edges which can be intersected by a plane (not containing any vertices of the polyhedron) if the polyhedron is convex.
(b) Prove that for a non-convex polyhedron this number i. can be as great as 9696, ii. cannot be as great as 100100.
(A Andjans, Riga