Multi-Colored DodecaHexaFlexagon with Full Explanation of Optimal Traverse, Nodes, and States

About a month ago, I stumbled onto two YouTube videos by Michael Anttila (see links below) where he showed a beautiful 12-sided hexaflexagon he'd painstakingly colored with colored pencils and ordered the faces and triangles in such a way as to be able to traverse through the optimal path by following each main color from its solid face. I flex differently from him and also fold slightly differently, so it took some experimentation on my part to figure out how to make my own version of his brilliant model.

This video is the result of numerous attempts, but I am pleased with the outcome. Along the way, I also tried using different papers, glues, and protective coverings to try to arrive at something that was durable and workable, but I believe that quest still needs exploration.

I wanted to map out all of the nodes and try to understand better the frequency of each of the types of faces (alpha, beta, and gamma), so I learned a great deal in the process. One of Michael's videos showed his mapping, but I didn't understand it as well as I hoped, so I had to make my own. In the end, I'm not sure why it was all such a Herculean effort for me, but I am glad I kept with it. I've often had issues with spatial relations and sometimes I just have to hack away at things until they start to make a tiny bit of sense.

When all was said and done, though, it wasn't until after videoing and editing it all that I realized I hadn't even used the largest version that I'd made specifically for those purposes!!! Oh well. Sometimes I just have to laugh at myself!

Thanks to Michael for the inspiration and clever and beautiful design. I hope to find a way to donate to him a little something to show my appreciation. I hope you all enjoy my explanations and glimpse into this journey.

Michael Anttila's Dodecahexaflexagon Walkthrough:    • Dodecahexaflexagon Walkthrough  
Michael Anttila's Dodecahexaflexagon Tutorial:    • Dodecahexaflexagon Tutorial