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. We made the pentagons with our Pentomizer, which uses OpenSCAD code to create pentagons from Ed Pegg's Wolfram Demonstration 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. This design has a Creative Commons Attribution Non-Commercial Share Alike 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.