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Theorems on tessellations by polygons

Journal Article · · Sbornik. Mathematics
 [1]
  1. International Institute of Earthquake Prediction Theory and Mathematical Geophysics, Russian Academy of Sciences, Moscow (Russian Federation)

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}.

OSTI ID:
21208318
Journal Information:
Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 6 Vol. 194; ISSN 1064-5616
Country of Publication:
United States
Language:
English

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