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Complete classification of reflexive polyhedra in four dimensions

Maximilian Kreuzer·Harald Skarke
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Abstract

Four dimensional reflexive polyhedra encode the data for smooth Calabi-Yau threefolds that are hypersurfaces in toric varieties, and have important applications both in perturbative and in non-perturbative string theory. We describe how we obtained all 473,800,776 reflexive polyhedra that exist in four dimensions and the 30,108 distinct pairs of Hodge numbers of the resulting Calabi-Yau manifolds. As a by-product we show that all these spaces (and hence the corresponding string vacua) are connected via a chain of singular transitions.

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Maximilian Kreuzer, Harald Skarke. 2000-02-28. Complete classification of reflexive polyhedra in four dimensions. https://arxiv.org/abs/hep-th/0002240

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