Geodesic
Convex pentagons which tile the plane (types: 11112, 11122)
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 478-530

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We consider the problem of classifying the convex pentagons that tile the plane edge-to-edge. It is proved that in each such tiling of the plane by pentagons, there exists a tile whose set of vertex degrees can be one of the following: (3,3,3,3,3), (3,3,3,3,4), (3,3,3,3,5), (3,3,3,3,6), (3,3,3,4,4). This provides the possibility of searching which finally leads to exhaustive classification of such pentagons. We consider convex pentagons types 11112, 11122.
Keywords: convex pentagon, tiling the plane, plane. 
@article{SEMR_2012_9_a15,
     author = {O. G. Bagina},
     title = {Convex pentagons which tile the plane (types: 11112, 11122)},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {478--530},
     publisher = {mathdoc},
     volume = {9},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2012_9_a15/}
}
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O. G. Bagina. Convex pentagons which tile the plane (types: 11112, 11122). Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 478-530. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a15/