  In the first part of this article we show for some examples of surfaces of
general type in toric 3-folds how to construct minimal and canonical models by
toric methods explicitly. The examples we study turn out to be surfaces of
general type, namely so called Kanev surfaces and Todorov surfaces. We show how
properties of our examples of surfaces could be derived directly from
properties of some polytopes and we compute the singularities of their
canonical models.
