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According to Batyrev, there are exactly 18 types of smooth toric Fano threefolds. As projective toric varieties, these are defined by the normal fan of certain 3-dimensional polytopes. Does anyone know of a reference where these polytopes are listed, e.g., as convex hulls of points?

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Google immediately finds Smooth toric fano varieties and their polytopes by A. Kasprzyk, which has pictures of the 18 polytopes. Surely following the references therein should get you coordinates of the vertices.

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    It probably is, and Kasprzyk probably knows where!2011-02-23