Geodesic
Simplicial 2-spheres obtained from non-singular complete fans
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 277-288 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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Yu. Suyama. Simplicial 2-spheres obtained from non-singular complete fans. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 277-288. http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a10/

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