five-fold tiling problem
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enThe trouble with five
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Craig Kaplan </div>
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Squares do it, triangles do it, even hexagons do it — but pentagons don't. They just won't fit together to tile a flat surface. So are there <i>any</i> tilings based on fiveness? <b>Craig Kaplan</b> takes us through the five-fold tiling problem and uncovers some interesting designs in the process. </div>
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<div class="pub_date">December 2007</div>
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<p>We are all familiar with the simple ways of tiling the plane by equilateral triangles, squares, or hexagons. These are the three <i>regular</i> tilings: each is made up of identical copies of a <i>regular polygon</i> — a shape whose sides all have the same length and angles between them — and adjacent tiles share whole edges, that is, we never have part of a tile's edge overlapping part of
another tile's edge.</p>
<p><!-- FILE: include/centrefig.html --></p><p><a href="http://plus.maths.org/content/trouble-five" target="_blank">read more</a></p>http://plus.maths.org/content/trouble-five#comments45Euclidean geometryfive-fold tiling problemgeometryhyperbolic geometrypenrose tilingspherical geometrysymmetrytilingSat, 01 Dec 2007 00:00:00 +0000plusadmin2319 at http://plus.maths.org/content