Classifying Fibers and Bases in Toric Hypersurface Calabi-Yau Threefolds

This dataset accompanies arXiv:2511.10601, "Classifying Fibers and Bases in Toric Hypersurface Calabi-Yau Threefolds", by F. Abbasi, R. Nally, and W. Taylor. In that work, we found a total of 2,264,992,252 toric genus-one and elliptic fibrations in the 473,800,776 four-dimensional reflexive polytopes in the Kreuzer-Skarke list. This Zenodo repository contains files summarizing all of these fibrations, in a format described in Section 3.4 of the the paper. As described in the paper, we split the entire Kreuzer-Skarke database (arXiv:hep-th/9805190, originally hosted at http://hep.itp.tuwien.ac.at/%7Ekreuzer/CY/CYcy.html) into chunks of no more than one million polytopes; we include these chunks in this repository for completeness. We provide the data in three separate organizational schemes, wherein we filter the fibrations by the number of vertices of the ambient polytope, the Hodge numbers of the ambient polytope, and the Morrison-Taylor class of the base of the fibration, respectively. We additionally include the code used to generate this data, which is also available on GitHub at https://github.com/wati4/fibers-public. 

The files included in this repository are:

all-fibers.zip (Primary output containing list of all 2.2G fibers)
bases.zip (fibers organized by base number)
Hodge.zip (fibers organized by Hodge number of CY3)
fibers-public-main.zip (Computer code to compute and analyze fibers; also on github)
KS_split.zip (Kreuzer-Skarke data from arXiv:hep-th/9805190 organized into blocks of max 1M polytopes)