  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.
