AlgTop9: Applications of Euler's formula and graphs

We use Euler's formula to show that there are at most 5 Platonic, or regular, solids. We discuss other types of polyhedra, including deltahedra (made of equilateral triangles) and Schafli's generalizations to higher dimensions. In particular in 4 dimensions there is the 120-cell, the 600-cell and the 24-cell. Finally we state a version of Euler's formula valid for planar graphs.

This is the ninth lecture in this beginner's course on Algebraic Topology, given by Assoc Prof N J Wildberger at UNSW. His other YouTube series are found at YouTube channel: njwildberger.