We construct small (50 and 26 points, respectively) point sets in dimension 5 whose graphs of triangulations are not connected. These examples improve our construction in J. Amer. Math. Soc. 13:3 (2000), 611–637 not only in size, but also in that their toric Hilbert schemes are not connected either, a question left open in that article. Additionally, the point sets can easily be put into convex...
