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There are many papers and books which study about the regular subdivision of a convex lattice polytope. My question is about "Non"-regular subdivisions of a 2-dimensional convex lattice polygon.

I came up with some statements about them and wonder what is the significance of the study about them.

My background is algebraic geometry and tropical geometry. Is there any significance of such subdivision in terms of algebraic geometry?

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Could you define your terms? What is a non-regular subdivision? –  Joseph O'Rourke Nov 16 '11 at 20:55
    
it's a subdivsion that doesn't come from lifting the vertices of the polytope into a higher dimension and then "looking up" to see the facets of the triangulation. –  Andy B Nov 17 '11 at 1:33
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