Geodesic
Convex pentagons which tile the plane (types: 11112, 11122)
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 478-530 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] Bagina O. G., “Mozaiki iz vypuklykh pyatiugolnikov”, Vestnik KemGU, 2011, no. 4(48), 63–73

[2] Bagina O., “Tiling the Plane with Congruent Equilateral Convex Pentagons”, J. Combin. Theory. Ser. A, 105:2 (2004), 221–232 | DOI | MR | Zbl

[3] Schattschneider D., “Tiling the Plane with Congruent Pentagons”, Math. Magazine, 51 (1978), 29–44 | DOI | MR | Zbl

[4] Sugimoto T., Ogawa T., “Systematic Study of Convex Pentagonal Tilings. I: Case of Convex Pentagons with Four Equal-length Edges”, Forma, 20 (2005), 1–18 | MR

[5] Stein R., “A new pentagon tiler”, Mathematics Magazine, 58 (1985), 308 | DOI | MR