| The goal of this thesis is to classify all K3 surfaces and Calabi-Yau threefolds that can be obtained as a complete intersection of two semi-ample line bundles in a Gorenstein toric Fano variety. We will find that this classification problem is equivalent to the classification of reflexive polytopes of index 2 in the dimension 5 and 6, respectively. This is a generalization of the result of H. Skarke and M. Kreuzer, in which they classified the reflexive polytopes in dimension 3 and 4.;In the process of classification, we will extensively use algorithms in the field of computational geometry, such as computing convex hull of a set of points and integral hull problem. PALP, C-language and MAGMA were the primary tools for the computation. |
