Geodesic
$k$-belts and edge-cycles of three-dimensional simple polytopes with at most hexagonal facets
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 197-213

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We describe the structure of $k$-belts on simple $3$-polytopes with at most hexagonal facets. As a corollary we prove that the number of patches that can be bounded by a simple edge-cycle of given length on such polytopes different from nanotubes, is finite. 
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     author = {N. Yu. Erokhovets},
     title = {$k$-belts and edge-cycles of three-dimensional simple polytopes with at most hexagonal facets},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {197--213},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a4/}
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N. Yu. Erokhovets. $k$-belts and edge-cycles of three-dimensional simple polytopes with at most hexagonal facets. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 2, pp. 197-213. http://geodesic.mathdoc.fr/item/DVMG_2015_15_2_a4/