Penrose P3 Tiles

prusaprinters

<p>Penrose tilings cover a surface in a pattern with some remarkable properties: they are aperiodic, have 5-fold symmetry, and are self-similar. There are several variations of Penrose tilings--this Thing contains the two tiles needed for the rhombus (P3) tiling.</p> <p>The edge of each tile has either a notch or a protrusion, which is either round or triangular. These notches and protrusions keep you from creating a repeating pattern when tiling. Round notches need to be lined up with round protrusions, and triangular notches with triangular protrusions. It is fairly easy to wind up with a "defect" where there's a spot no tile can fit.</p> <p>For more information, see the Wikipedia article, <a href="http://en.wikipedia.org/wiki/Penrose_tiling">http://en.wikipedia.org/wiki/Penrose_tiling</a> (also the source for the pattern I used), and these two more technical discussions: <a href="http://www.ams.org/samplings/feature-column/fcarc-penrose">http://www.ams.org/samplings/feature-column/fcarc-penrose</a> and <a href="http://www.ams.org/samplings/feature-column/fcarc-ribbons">http://www.ams.org/samplings/feature-column/fcarc-ribbons</a></p> <p>Note that a proper Penrose tiling will require about 16 large tiles for every 10 small tiles, so if you just print a bunch of this file you will have an excess of small tiles.</p> <h3>Instructions</h3> <ol> <li>Print a bunch of tiles. On my Up I can print 9 copies of this file (18 tiles total) at once; you'll probably want at least twice that number to really play with them.</li> <li>Fit together, being careful to match rounds to rounds and triangles to triangles.</li> </ol> Category: Other