# Fibration structure in toric hypersurface Calabi-Yau threefolds

## TL;DR

This paper systematically analyzes 4D reflexive polytopes and finds that most Calabi-Yau threefolds derived from them possess elliptic or genus one fibrations, supporting the idea that such fibrations are common.

## Contribution

It provides a comprehensive analysis showing that nearly all 4D reflexive polytopes have a 2D reflexive subpolytope, indicating widespread elliptic or genus one fibrations in Calabi-Yau threefolds.

## Key findings

- Almost all polytopes have a 2D reflexive subpolytope
- Most Calabi-Yau threefolds have elliptic or genus one fibrations
- Supports the hypothesis of prevalent elliptic fibrations in Calabi-Yau threefolds

## Abstract

We find through a systematic analysis that all but 29,223 of the 473.8 million 4D reflexive polytopes found by Kreuzer and Skarke have a 2D reflexive subpolytope. Such a subpolytope is generally associated with the presence of an elliptic or genus one fibration in the corresponding birational equivalence class of Calabi-Yau threefolds. This extends the growing body of evidence that most Calabi-Yau threefolds have an elliptically fibered phase.