Pentomizer - Every known tessellating convex pentagon by mathgrrl

Last crawled date: 3 years, 1 month ago

With this Customizer you can print ALL OF THE PENTAGONS. All of the good ones, that is. That we know of. Fifteen types of pentagons, including one discovered by mathematicians only this year!
What?
"All of the good ones" means all of the irregular convex pentagons that tile, or tessellate, the plane.
"That we know of" means that since 1918, mathematicians have been trying to find all possible tessellating pentagons, and this Customizer can make all of the ones that have been found so far.
"Fifteen types" means that there are fifteen classes of tessellating pentagons, where each of these classes might include just one pentagon, or might include infinitely many somewhat similar-looking pentagons.
"Only this year" means that THIS YEAR, after a thirty-year dry spell in which no new tessellating pentagon types had been found, mathematicians Mann, McLoud, and Von Derau of the University of Washington Bothell found a new one!
But what can you MAKE with this design, and how?
Press the "Open in Customizer" button to get started
Choose one of the fifteen types of pentagon
Decide whether you want to use your tessellating pentagon to make a pattern, a puzzle, a picture, a container, a desk organizer, or even a cookie cutter!
Change side lengths and angles within the restrictions of the pentagon class, if possible (most sliders only work on certain classes); use restraint if you want to preserve convexity or five-sidedness
Press the "Create Thing" button and then download and print your pentagon design
Take a photo, click "I Made One" on this page, and upload your photo to show off your pentagon creation
UPDATE: If you'd like to be able to set some of the desk organizer heights to zero, check out SpoonUnit's remix.
References:
Vertex and offset data for each pentagon class were adapted from Ed Pegg's fantastic Wolfram Demonstration Pentagon Tilings
Mathematical facts and history about the fifteen pentagon classes can be found on Wikipedia at Pentagonal tiling
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This design and all associated pictures and files are licensed under the Creative Commons Attribution Non-Commercial Share Alike license. If you want to use designs, images, or files outside of the terms of this license, please email request@mathgrrl.com.