Convex Polytopes: A group theoretic and a graph theoretic perspective
We present classical results for convex polytopes. After reviewing quaternions, we apply these algebraic tools to polyhedral graphs. In 1891, Eberhard wondered if there exists a trivalent polyhedron with an odd number of multitrivalent faces. In 1964, Motzkin was able to find a solution to the problem. He used the group formed by the 24 units in the ring of Hurwitz quaternion integers to obtain th
