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Q&A #6201 |
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Dear Anna, Only three regular polygons tessellate in the Euclidean plane: triangles, squares or hexagons. Since the regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees. This works for the triangle, square, and hexagon, and you can show working tessellations for these figures. For all the others, the interior angles are not exact divisors of 360 degrees, and therefore those figures cannot tile the plane. I have more information on this page: http://mathforum.org/sum95/suzanne/whattess.html and it includes diagrams that I think are useful for understanding. The full site, Tessellation Tutorials, that I started in 1995 is here: http://mathforum.org/sum95/suzanne/tess.intro.html I hope that helps. -Suzanne A., for the T2T service
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