Calabi-Yau data

Reflexive polyhedra in 4 dimensions

There are 473,800,776 reflexive polyhedra in 4 dimensions
(cf. hep-th/0002240, math.AG/0001106).

The complete list is also available

in the form of 30 gzipped ascii files v05.gz, ...,v33.gz and v36.gz (each file contains all reflexive 4-polytopes with the number of vertices corresponding to the file name), and
in Parquet format (at the Hugging Face Hub).

The different Hodge numbers [h11 h12 chi] are listed in separate files for

7,555 hypersurfaces in WPs [2,780 Hodge data],

184,026 IP weight systems [10,237 Hodge data],

473,800,776 reflexive polyhedra [30,108 Hodge data].

Weight systems and r-maximal polytopes (for explanations see CS/WS):
There are

184,026 single IP weight systems
You can search for Hodge numbers among the corresponding polytopes:

16,040 CWS of the type 4+4 (non-trivial)

1,122 CWS of the type 3+4 (non-trivial)

6 CWS of the type 3+3 (trivial)

36 CWS of the type 3+3+3 (non-trivial)

116 CWS from combining the (C)WS for d=3 trivially with (1,1);

308 of the above are r-minimal (C)WS.
There are 25 further r-maximal polytopes.

K3 fibered toric CY hypersurfaces
The Newton polyhedra and Calabi-Yau hypersurfaces corresponding to the 184,026 IP weight systems were analysed in hep-th/9610154. Informations on Hodge and fibration data, as well as numbers of points and vertices in the M and N lattices, are encoded in the following files:

All 184,026 weights (2.37 MB, uncompressed 10.6 MB),

subset with lowest degrees (356 kB),

subset with highest degrees (54 kB).

The files contain lines of the form

   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

encoding general data

5 weights and their sum, the degree d;

TS means Transverse (7555 lines) and that the Newton polytope Spans the coordinate hyperplanes (38727 lines);
other cases are `non-transverse reflexive' and/or `non-spanning';

Hodge numbers are listed as h11 and h12,

M: p v and N: p v are the numbers of points and vertices of the Newton polytope and of its dual, respectively;

and fibration data

P: p indicates the number p of reflexive projections, which correspond to K3 fibrations (P: - if unknown).
F: f indicates the number f of projections onto reflexive facets. For f>0 the last f numbers denote the weights whose coordinate hyperplanes carry the K3 facets.