From: Suzanne A. (for Teacher2Teacher Service)
Date: Apr 25, 2001 at 10:11:56
Subject: Re: Tessellations shapes

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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