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Complete classification of reflexive polyhedra in four dimensions

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arxiv hep-th/0002240 v1 pith:7O2N6PMS submitted 2000-02-28 hep-th math.AG

classification hep-thmath.AG
keywords fourpolyhedrareflexivecalabi-yaudimensionsstringapplicationsby-product
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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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