five-fold tiling problem
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enA five that fits
https://plus.maths.org/content/five-fits
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<p>A brand-new pentagon to tile your wall with.</p>
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<p>Mathematicians have found a new type of pentagon you can tile the plane with. It's a nice result because pentagons are famously awkward when it comes to tiling. The most natural pentagon to think about is the <em>regular</em> one, whose sides all have the same length. But you won't ever get this one to tile your bathroom wall. If you try to fit several copies around a point so that they all meet at a corner, you will find that three leave a gap, and four create an overlap:</p><p><a href="https://plus.maths.org/content/five-fits" target="_blank">read more</a></p>https://plus.maths.org/content/five-fits#commentsaperiodic tilingfive-fold tiling problemgeometrytilingFri, 14 Aug 2015 15:29:14 +0000mf3446420 at https://plus.maths.org/contentThe trouble with five
https://plus.maths.org/content/trouble-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="https://plus.maths.org/content/trouble-five" target="_blank">read more</a></p>https://plus.maths.org/content/trouble-five#comments45Euclidean geometryfive-fold tiling problemgeometryhyperbolic geometrypenrose tilingspherical geometrysymmetrytilingSat, 01 Dec 2007 00:00:00 +0000plusadmin2319 at https://plus.maths.org/content