Theorems on tessellations by polygons
Abstract
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.
- Publication:
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Sbornik: Mathematics
- Pub Date:
- June 2003
- DOI:
- 10.1070/SM2003v194n06ABEH000743
- Bibcode:
- 2003SbMat.194..879G