Geodesic
Simplicial 2-spheres obtained from non-singular complete fans
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 277-288.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DVMG_2015_15_2_a10,
     author = {Yu. Suyama},
     title = {Simplicial 2-spheres obtained from non-singular complete fans},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {277--288},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a10/}
}
TY  - JOUR
AU  - Yu. Suyama
TI  - Simplicial 2-spheres obtained from non-singular complete fans
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2015
SP  - 277
EP  - 288
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a10/
LA  - en
ID  - DVMG_2015_15_2_a10
ER  - 
%0 Journal Article
%A Yu. Suyama
%T Simplicial 2-spheres obtained from non-singular complete fans
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2015
%P 277-288
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a10/
%G en
%F DVMG_2015_15_2_a10
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/

[1] G. Brinkmann and B. D. McKay, “Construction of planar triangulations with minimum degree 5”, Discrete Math., 301 (2005), 147–163 | DOI | MR | Zbl

[2] C. Delaunays, “On hyperbolicity of toric real threefolds”, Int. Math. Res. Not., 2005, no. 51, 3191–3201 | DOI | MR

[3] M. W. Davis and T. Januszkiewicz, “Convex polytopes, Coxeter orbifolds and torus actions”, Duke Math. J., 62 (1991), 417–451 | DOI | MR | Zbl

[4] T. Oda, Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties, Ergeb. Math. Grenzgeb. (3), Springer-Verlag, Berlin, 1988 | MR | Zbl