{"id":2543,"date":"2014-02-17T20:51:02","date_gmt":"2014-02-18T01:51:02","guid":{"rendered":"https:\/\/zingman.com\/blog\/?p=2543"},"modified":"2014-02-17T20:51:02","modified_gmt":"2014-02-18T01:51:02","slug":"more-with-penrose-tessellations","status":"publish","type":"post","link":"https:\/\/www.zingman.com\/blog\/2014\/02\/17\/more-with-penrose-tessellations\/","title":{"rendered":"Expanded Penrose Tessellations with Robots"},"content":{"rendered":"

Believe it or not we had two more snow days this week! On Thursday I broke my snowblower clearing out 15\u201d or wet, heavy stuff. Thursday night was had more snow and Friday it turned to rain, and then more snow for a slushy and mess. Oy! Well the weekend came and some sunshine, and a chance to get caught up on my rest. And the Olympics are on. I never really get into the summer games very much, but I do enjoy the winter games. In any event, I\u2019m sure everyone is looking forward to spring.<\/p>\n

My origami friends Brian and Beth are going to be getting together at a maker event next week, where they will have access to a large cutting machine. Brian asked me if I could provide a cutter-ready file of the crease pattern for one of my Penrose tessellations. When I worked on this before, folding by hand, I did the first three expansions, creation patterns with 10, 35 and 70 cells. With the prospect of the machine doing the scoring, larger tessellations become feasible. I created CP\u2019s for the next two expansions, which come out to 105 and 175 tiles. These numbers are really interesting, because they are all multiples of 5 and 7. 2 x 5 =10, 5 x 7 =35, 2 x 5 x 7 =70, 3 x 5 x 7 =105, and 5 x 5 x 7 =175. You\u2019d expect five, but it\u2019s very strange how seven figures prominently as well.<\/p>\n

As for the CPs, I was able to dispense with all the landmarks and only include creases that appear in the final model. This ought to make the folding go much faster as well as providing a cleaner appearance. In addition, I shortened all the line segments so that the intersections don\u2019t get scored, to avoid weakening the paper. Lastly, I color coded the creases so that the facets are blue, the ridges between the are red, and the creases for collapsing the intersections are grey. This was fairly time consuming, an unexpected but fun little project. Good for waiting for the snow to melt and watching the Olympics. Having worked the CP out to 175 I think I\u2019m done with this for a while. If you\u2019re an origami person with access to a cutting machine and are interested in trying one of the patterns, please feel free to contact me. Meanwhile, I\u2019m looking forward to seeing how Brian and Beth\u2019s experiment comes out.<\/p>\n

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Believe it or not we had two more snow days this week! On Thursday I broke my snowblower clearing out 15\u201d or wet, heavy stuff. Thursday night was had more snow and Friday it turned to rain, and then more snow for a slushy and mess. Oy! Well the weekend came and some sunshine, and … Continue reading “Expanded Penrose Tessellations with Robots”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,16],"tags":[],"class_list":["post-2543","post","type-post","status-publish","format-standard","hentry","category-origami","category-people"],"_links":{"self":[{"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/posts\/2543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/comments?post=2543"}],"version-history":[{"count":0,"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/posts\/2543\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/media?parent=2543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/categories?post=2543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.zingman.com\/blog\/wp-json\/wp\/v2\/tags?post=2543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}