Combinatorial tilings of the sphere by pentagons
The electronic journal of combinatorics, Tome 20 (2013) no. 1
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent pentagons. We show that the tiling cannot have only one vertex of degree $>3$. Moreover, we construct earth map tilings, which give classifications under the condition that vertices of degree $>3$ are at least of distance $4$ apart, or under the condition that there are exactly two vertices of degree $>3$.A corrigendum was added to this paper on 16th April 2014.
DOI :
10.37236/2892
Classification :
05B45, 52C20
Mots-clés : combinatorial tiling, sphere tiling, pentagon
Mots-clés : combinatorial tiling, sphere tiling, pentagon
Affiliations des auteurs :
Min Yan 1
@article{10_37236_2892,
author = {Min Yan},
title = {Combinatorial tilings of the sphere by pentagons},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2892},
zbl = {1267.05062},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2892/}
}
Min Yan. Combinatorial tilings of the sphere by pentagons. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2892
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