Classification of reflexive polyhedra in three dimensions

This is the authors' abstract. We don't add key points for this paper.

We present the last missing details of our algorithm for the classification of reflexive polyhedra in arbitrary dimensions. We also present the results of an application of this algorithm to the case of three dimensional reflexive polyhedra. We get 4319 such polyhedra that give rise to K3 surfaces embedded in toric varieties. 16 of these contain all others as subpolyhedra. The 4319 polyhedra form a single connected web if we define two polyhedra to be connected if one of them contains the other.