Polyhedra and Euler's Formula - Algebraic Topology

Explore the fascinating world of polyhedra and Euler's formula in this eighth lecture of a beginner's course on Algebraic Topology. Investigate the five Platonic solids: tetrahedron, cube, octahedron, icosahedron, and dodecahedron. Learn about Euler's formula, which relates the number of vertices, edges, and faces in polyhedra. Follow along as the lecturer provides a proof using a triangulation argument and demonstrates the concept of flow down a sphere. Gain insights into Archimedean solids, including the soccer ball, and delve into the complexities of spheres and counting techniques. Discover the intricacies of flow lines and arrive at the final result in this comprehensive exploration of geometric structures.

Introduction
Polyhedra
Cube Icosahedron
Eulers formula
Archimedean solids
How many are there
The soccer ball
The sphere
The complex
Counting the complex
Flow lines
Final result