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.