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Calabi-Yau Volumes and Reflexive Polytopes

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Figure

Fig. 1. The 16 inequivalent reflexive polytopes �2 in dimension 2. We see that, in particular, this includesthe toric del Pezzo surfaces, numbers 1, 4, 3, 6, 10, which are the 5 smooth ones
Table 1. The number of inequivalent reflexive polytopes in different dimensions. The reflexive polytopes allgive toric Gorenstein Fano varieties and the regular ones, smooth toric Fano n-folds
Fig. 3. Two different constructions of Calabi–Yau varieties from a reflexive polytope �n
Table 2. The various brane configurations for brane tilings and how, under T-duality, they map to D-branes(c) Brane hyper-brick models where Euclidean D3-branes are suspended between a NS5-brane that wraps aholomorphic 4-cycleprobing affine Calabi–Yau cones
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