Far Eastern Mathematical Journal

To content of the issue

Simplicial 2-spheres obtained from non-singular complete fans

Yusuke Suyama

2015, issue 2, . 277-287

We prove that a simplicial 2-sphere satisfying a certain condition is the underlying simplicial complex of a 3-dimensional non-singular complete fan. In particular, this implies that any simplicial 2-sphere with $\leq 18$ vertices is the underlying simplicial complex of such a fan.

triangulation, fan, toric topology

Download the article (PDF-file)


[1] G. Brinkmann and B.D. McKay, "Construction of planar triangulations with minimum degree 5", Discrete Math., 301 (2005), 147-163.
[2] C. Delaunays, "On hyperbolicity of toric real threefolds", Int. Math. Res. Not., 2005, 51, 3191-3201.
[3] M.W. Davis and T. Januszkiewicz, "Convex polytopes, Coxeter orbifolds and torus actions", Duke Math. J., 62 (1991), 417-451.
[4] T. Oda, Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties, Ergeb. Math. Grenzgeb. (3), Springer-Verlag, Berlin, 1988.

To content of the issue