What is… Steinitz' Theorem?

Where & When

• Friday, April 26, 2019, 1pm @ Urania BMS Loft (3rd floor)

Abstract

• Steinitz' theorem states that a graph is the graph of a 3-dimensional polytope if and only if it is simple, planar, and 3-connected. In this What Is seminar we cover the notions in the theorem and the proof of the easier implication. We discuss polytopes and their graphs, and we look at Schlegel diagrams and d-connected graphs. We sketch a proof of Balinski's theorem stating that the graph of a d-dimensional polytope is d-connected.