Geodesic
Theorems on tessellations by polygons
Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 879-895 Cet article a éte moissonné depuis la source Math-Net.Ru

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What general regularity manifests itself in the fact that a triangle, and in general any convex polygon, cannot be tessellated by non-convex quadrangles? Another question: it is known that for $n>6$ the plane cannot be tessellated by convex $n$-gons if their diameters are bounded, while the areas are separated from zero; can this fact be generalized for non-convex polygons? In the present paper we introduce the characteristic $\chi(M)$ of a polygon $M$. We answer the above questions in terms of $\chi(M)$ and then study tessellations of the plane by $n$-gons equivalent to $M$, that is, with the same sequence of angles greater than and smaller than $\pi$. 
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     author = {M. L. Gerver},
     title = {Theorems on tessellations by polygons},
     journal = {Sbornik. Mathematics},
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     year = {2003},
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     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_6_a4/}
}
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M. L. Gerver. Theorems on tessellations by polygons. Sbornik. Mathematics, Tome 194 (2003) no. 6, pp. 879-895. http://geodesic.mathdoc.fr/item/SM_2003_194_6_a4/

[1] Fulton Candler., “Tessellations”, Amer. Math. Monthly, 99:3 (1992), 442–445 | DOI | MR | Zbl

[2] Prasolov V. V., Zadachi po planimetrii, Chast II, Nauka, M., 1991 | MR | Zbl

[3] Gerver M. L., Parkety i mozaiki, , http://www.mccme.ru/olympiads/lktg/2000/http://www.mccme.ru/olympiads/lktg/2000/mosaic.ps