A complete list of the Hodge data of Calabi-Yau threefolds described by hypersurfaces in toric varieties has been obtained by Avram, Kreuzer, Mandelberg and Skarke in ref. hep-th/9610154. This paper also contains a fibration flags for those threefolds that are K3 fibrations.

The data of the 184026 toric weight configurations analyzed in this paper is contained in the following 2.4mb file .

The notation of the list

    1 1 1  1  1   5=d  TS  H: 1 101  M:126  5  N: 6  5  P:0  F:0
    3 4 5  6  8  26=d  rS  H:14  24  M: 32 14  N:19 10  P:-  F:1  6
    1 3 3 10 14  31=d  Tn  H:14 106  M:143  9  N:21  7  P:0  F:0
    4 7 7 10 12  40=d  rn  H:28  16  M: 23  7  N:25  6  P:3  F:2  7 12

• the first 5 entries describe the weights, which add up to the sixth, the degree.
• T stands for transverse (there are 7,555 configuration of this type).
• S indicates that the polytope spans the coodinate hyperplanes (this applies to 38727 configurations).
• the two numbers following the symbol H are the Hodge numbers of the corresponding Calabi-Yau threefold.
• M: p n denote the number of points and vertices for the Newton polytope M and its dual N respectively.
• P: n denotes the number of possible reflexive projections of the polytope, describing the number of possible K3 fibrations (an `-' indicates that this number is not known).
• F: n ndicates the number f of projections onto reflexive facets. For f>0 the last f numbers denote the weights whose coordinate hyperplanes carry the K3 faces.