Tessellating Pentagons

thingiverse

Each of these fifteen irregular pentagons will perfectly tessellate a plane with copies of itself. In other words, you can tile your bathroom wall fifteen different ways with these weird-shaped pentagon tiles! The pentagons are sized to have the same areas, and each pentagon is a representative of one of the fifteen families of tessellating pentagons as described on [Wikipedia](https://en.wikipedia.org/wiki/Pentagonal_tiling). We made the pentagons with our [Pentomizer](https://www.thingiverse.com/thing:1008750), which uses OpenSCAD code to create pentagons from Ed Pegg's [Wolfram Demonstration](http://demonstrations.wolfram.com/PentagonTilings/) vertex data. Each type of pentagon can be combined with itself to form a 3-, 4-, 6-, 8-, or 12-tile unit that tessellates the plane using only translations. Those units are also included here, and can be used as guides to start the pentagonal tessellations. Don't have a 3D printer, or have a pentagon emergency? You can order printed sets of these pentagons from our [Shapeways shop](https://www.shapeways.com/shops/mathgrrl?section=Pentagon+Collection&s=0). *** **Twitter: [twitter.com/mathgrrl](https://twitter.com/mathgrrl)** **Hacktastic blog: [www.mathgrrl.com/hacktastic](http://www.mathgrrl.com/hacktastic)** **Shapeways store: [www.shapeways.com/shops/mathgrrl](https://www.shapeways.com/shops/mathgrrl)** *This design has a [Creative Commons Attribution Non-Commercial Share Alike](https://creativecommons.org/licenses/by-nc-sa/2.5/) license, which means that you can print, remix, and use this model with design credit to mathgrrl, but if you want to sell something then you should ask first, at <request@mathgrrl.com>.* ***