This web-page contains the result of computation of the number of fine triangulations for the reflexive 4-polytopes corresponding to Batyrev's Calabi-Yau varieties with h^{1,1} ≥ 300.

The file polytopes_full_normalized_nft.txt
contains a list of 401 items. Each item corresponds to a reflexive 4-polytopes P with h^{1,1} ≥ 300. It is of the form {V,F2} where:

• V is the list of vertices of P;

• F2 is the list whose items correspond to 2-faces of P. Each item is of the form {f,n} where f is a planar lattice polygon isomorphic to the 2-face and n is the number of its fine triangulations. The polygons representing the 2-faces are chosen so that it is easy to see whether one 2-face can be embedded to another by an affine lattice isomorphism.

The file lwa.txt
contains a list whose items correspond to 2-faces. Each item is of the form {{A,L},f,n,u} where:

• A is the area (normalized so that the area of the unit square is 2);

• L is a list of lattice lengths of consecutive sides of the 2-face. The initial point and the direction of circuit along the boundary are chosen so that L is minimal possible for the lexicographic order.

• f and n are as above;

• u is a list of references to the list of reflexive 4-polytopes. Its items are of the form {i,j} which means that this polygon appear as the j-th 2-face of the i-th reflexive 4-polytope. The 4-polytopes and their 2-faces are numbered starting from 1.

The file nft.txt
contains a list of numbers. Its i-th element is the total number of fine triangulations of the 2-faces of the i-th reflexive polytope, i.e. the product of these numbers over the 2-faces of the i-th polytope.