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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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 
@article{UZKU_2012_154_1_a17,
     author = {M. N. Matveev},
     title = {A minimal nonpolytopal fan},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {202--207},
     year = {2012},
     volume = {154},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a17/}
}
TY  - JOUR
AU  - M. N. Matveev
TI  - A minimal nonpolytopal fan
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2012
SP  - 202
EP  - 207
VL  - 154
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a17/
LA  - ru
ID  - UZKU_2012_154_1_a17
ER  - 
%0 Journal Article
%A M. N. Matveev
%T A minimal nonpolytopal fan
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2012
%P 202-207
%V 154
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2012_154_1_a17/
%G ru
%F UZKU_2012_154_1_a17
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/

[1] Cains S. S., “Isotropic deformation of geodesic complexes on the 2-sphere and on the plane”, Ann. Math., 45 (1944), 207–217 | DOI | MR

[2] Supnick F., “On the perspective deformation of polyhedra. II. Solution of the convexity problem”, Ann. Math., 53:3 (1951), 551–555 | DOI | MR | Zbl

[3] Matveev M. N., “Nevidimye grani i porozhdayuschie mnogogranniki”, Trudy MFTI, 3:1 (2011), 102–106

[4] Aurenhammer F., “A criterion for the affine equivalence of cell complexes in $\mathbb R^d$ and convex polyhedra in $\mathbb R^{d+1}$”, Discrete Comput. Geom., 2:1 (1987), 49–64 | DOI | MR | Zbl

[5] Shephard G. C., “Spherical complexes and radial projections of polytopes”, Israel J. Math., 9:2 (1971), 257–262 | DOI | MR | Zbl

[6] Ziegler G. M., Lectures on polytopes, Springer-Verlag, Berlin et al., 1995, ix+370 pp. | MR

[7] De Loera J. A., Rambau J., Santos F., Triangulations. Structures for algorithms and applications, Springer-Verlag, Berlin et al., 2010, xiv+535 pp. | MR | Zbl

[8] Betke U., Schulz C., Wills J. M., “Bänder und möbiusbänder in konvexen polytopen”, Abh. Math. Sem. Univ. Hamburg, 44 (1975), 249–262 | DOI | MR