|
Take n points in space, connect them by straight lines and immerse this structure in a soap solution. The "bubble" that you get is called a 3-dimensional (convex) polytope. It has vertices (corners), edges, and faces, so let's count their numbers and denote them by, say, (V,E,F). What can we say about all triples of integers we can obtain in this way? A complete answer to this question was given by Steinitz about 100 years ago. In this lecture we will try to rediscover it on our own! |