Azer Akhmedov, NDSU

Math Club, October 24^th.

Title:  Who invented the soccer ball.

Abstract:  The soccer ball is a highly mathematical object: it is a convex polyhedron made of pentagons and hexagons. Moreover, at every vertex there exist exactly one pentagon and two hexagons. Thus any two vertices look locally the same.

 Can one find all (convex) polyhedra where any two vertices look the same, i.e. we have the same polygons at every vertex with the same pattern? Obviously, Platonic solids (e.g. tetrahedron, cube) are such examples but are there many more? 

 In the talk, we will give a complete answer to this question.