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?
Toric fano threefolds
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algebraic-geometry
1 Answers
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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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0Thanks for the link, I already looked at that paper. The pictures are nice, but it is hard to make out what the polytope is explicitly. The references there refer to Batyrev's original paper, which I cannot find anywhere. – 2011-02-23
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0@user6064: you can always ask the author, you know: he surely knows the coordinates :) – 2011-02-23
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0Sure I could do that, but since this is so well-known, I was hoping it would be on-line somewhere :) – 2011-02-23
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0It probably is, and Kasprzyk probably knows where! – 2011-02-23