Step 1: Gather Materials
There are two parts to this project. One process occurs in the bits world and the other, in the world of atoms. Below is a materials list for what you'll need to finish this project. I've separated the necessary tools just in case you're solely interested in either the wallet, or scripting for illustrator :
Adobe Illustrator CS6
Adobe Extend Script Toolkit
Epitrochoid script (you can grab this from my Github)
You can also just use my vector file and skip the scripting bit if you'd like to!
Laser Cut Wallet:
12x24 piece of 1/8" thick acrylic
1/4" Bookbinding screw post
Super Glue or epoxy with fine tip
Access to a laser cutter. Make Mode is great if you're looking for a service that can supply materials!
Step 2: Scripting in Illustrator
Experiment and have fun with Extend Script. You can make quick and complex vector art if you have a few moments to kill.
Step 3: Implementing the Epitrochoid script
Now that you're synced up, enter the epitrochoid script into ExtendScript.
If you'd like to avoid coding, you can simply open up the vector file. Play with the settings or vector art to make something that suits you! To learn more about parametic equations and epitrochoids, Wikipedia is very helpful.
Step 4: Laser Cutting
For an Epilog laser cutter, you can color code between raster and cut. Essentially, you want to raster the details and laser cut the actual wallet shapes. If you outsource, you should be able to have a pro do your settings. Make sure the raster is at least 1/4 of the normal power as these shapes have hundreds of lines and will chew up the acrylic otherwise (see above).
Step 5: Assembly!
The assembly is very straight forward. Glue or epoxy the 3 walls to the back (my back piece has the code for the epitrochoids). Glue together the three top pieces altering curved edges. Glue this to the back as well. Once the bottom piece is finished, add the binding element and washer through the pre-cut hole. Screw everything in tight enough for tension. I attempted using a magnet for closure, but tension seems to work best.
Step 6: Fin!
Let your wallet dry for 24 hours before use and it might be helpful to add a drop of epoxy/glue under each binding element to keep tension.