2000/02/28 by Maximilian Kreuzer, Harald Skarke · 10 citations
Physics and Astronomy · Mathematics · #hep-th #math.AG
published as Adv.Theor.Math.Phys. 4 (2002) 1209-1230 · 22 pages, latex2e
arxiv created 2000/02/28 · arxiv updated 2009/11/30
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.