Geodesic
Truncations of simple polytopes and applications
Informatics and Automation, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 115-144 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce and analyze truncation operations on simple polytopes. The results obtained allow us to describe relations between various classes of polytopes. Special attention is paid to three-dimensional polytopes and, first of all, fullerenes. 
@article{TRSPY_2015_289_a6,
     author = {V. M. Buchstaber and N. Yu. Erokhovets},
     title = {Truncations of simple polytopes and applications},
     journal = {Informatics and Automation},
     pages = {115--144},
     year = {2015},
     volume = {289},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2015_289_a6/}
}
TY  - JOUR
AU  - V. M. Buchstaber
AU  - N. Yu. Erokhovets
TI  - Truncations of simple polytopes and applications
JO  - Informatics and Automation
PY  - 2015
SP  - 115
EP  - 144
VL  - 289
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2015_289_a6/
LA  - ru
ID  - TRSPY_2015_289_a6
ER  - 
%0 Journal Article
%A V. M. Buchstaber
%A N. Yu. Erokhovets
%T Truncations of simple polytopes and applications
%J Informatics and Automation
%D 2015
%P 115-144
%V 289
%U http://geodesic.mathdoc.fr/item/TRSPY_2015_289_a6/
%G ru
%F TRSPY_2015_289_a6
V. M. Buchstaber; N. Yu. Erokhovets. Truncations of simple polytopes and applications. Informatics and Automation, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 115-144. http://geodesic.mathdoc.fr/item/TRSPY_2015_289_a6/

[1] Volodin V. D., “Kombinatorika flagovykh simplitsialnykh 3-mnogogrannikov”, UMN, 70:1 (2015), 181–182 | DOI | MR

[2] Deza M., Dyutur Sikirich M., Shtogrin M. I., “Fullereny i disk-fullereny”, UMN, 68:4 (2013), 69–128 | DOI | MR | Zbl

[3] Erokhovets N. Yu., “Gipoteza Gala dlya nestoedrov, otvechayuschikh polnym dvudolnym grafam”, Tr. MIAN, 266, 2009, 127–139 | MR | Zbl

[4] Lord E. E., Makkei A. L., Ranganatan S., Novaya geometriya dlya novykh materialov, Fizmatlit, M., 2010

[5] Tsigler G. M., Teoriya mnogogrannikov, MTsNMO, M., 2014

[6] Brinkmann G., Dress A. W. M., “A constructive enumeration of fullerenes”, J. Algorithms, 23:2 (1997), 345–358 | DOI | MR

[7] Eberhard V., Zur Morphologie der Polyeder, B. G. Teubner, Leipzig, 1891

[8] Brückner M., Vielecke und Vielflache: Theorie und Geschichte, B. G. Teubner, Leipzig, 1900 | Zbl

[9] Buchstaber V. M., Volodin V. D., “Combinatorial 2-truncated cubes and applications”, Associahedra, Tamari lattices and related structures, Tamari memorial Festschrift, Prog. Math., 299, Birkhäuser, Basel, 2012, 161–186 | MR | Zbl

[10] Grünbaum B., Convex polytopes, Grad. Texts Math., 221, Springer, New York, 2003 | MR | Zbl

[11] Volodin V. D., Combinatorics of flag simplicial 3-polytopes, E-print, 2012, arXiv: 1212.4696[math.CO] | DOI | MR