Truncations of simple polytopes and applications
Informatics and Automation, Selected issues of mathematics and mechanics, Tome 289 (2015), pp. 115-144.

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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.
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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