Geodesic
A minimal nonpolytopal fan
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 202-207

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The paper defines a polytopal incomplete fan as a subfan of a polytopal complete fan. A criterion for a not necessarily complete fan to be polytopal is proved. Using this criterion, a minimal nonpolytopal fan of three two-dimensional cones pairwise meeting in the origin is found in $\mathbb R^3$.
Keywords: polytopes, cones, systems of linear equations and inequalities.
Mots-clés : fans 
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     title = {A minimal nonpolytopal fan},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     volume = {154},
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     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a17/}
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M. N. Matveev. A minimal nonpolytopal fan. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 1, pp. 202-207. http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a17/