  We present two methods for studying fibrations of Calabi-Yau manifolds
embedded in toric varieties described by single weight systems. We analyse
184,026 such spaces and identify among them 124,701 which are K3 fibrations. As
some of the weights give rise to two or three distinct types of fibrations, the
total number we find is 167,406. With our methods one can also study elliptic
fibrations of 3-folds and K3 surfaces. We also calculate the Hodge numbers of
the 3-folds obtaining more than three times as many as were previously known.
