A Minimal Irreducible Triangulation of S3
نویسنده
چکیده
We present a very symmetric triangulation of the 3-sphere, where every edge is in at most five facets but which is not the boundary of a polytope. This shows that not every triangulation of a sphere, where angles around faces of codimension two are less than 2π in the metric pieced together by regular Euclidean simplices, is polytopal. The counterexample presented here is the smallest triangulation of S3 where every edge is contained in an empty triangle. Moreover, it shows that a triangulation of S3 that is embeddable into R4 with straight faces is not necessarily weakly vertex-decomposable.
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