Discrete Math - Applications of Euler's Polyhedra Formula

Discrete Math - Rose - MBHS - Blair - We review the geometric proof that there are only 5 Platonic solids and then use Euler's Polyhedra Formula to give a purely topological proof, including digressions into regular Euclidean tilings. Then we compute the number of vertices, faces, and edges for a few polyhedra based on their Schlafli symbol. Finally we precisely define the degree of a region and use Euler's formula to prove that K₅ is nonplanar. 5/15/2021