3D models of the unfoldings of the hypercube?

I implemented the ideas in the paper using Mathematica. I pushed it a bit further to actually generate the images below. You can download this Mathematica notebook to see the code and detailed explanation.

You might notice Dali's original in the middle of the third row from the bottom.

I used sage to make a 3d animation of all 261 unfoldings.

Here is a screenshot of the first few:

The file cube-unfoldings.txt contains all the unfoldings, each line contains a list of 8 points.

Edit: By popular, I add the (poorly commented) code:

unfolding the hypercube.ipynb: a jupyter notebook with sage code to generate the pairings for the unfoldings together and find the embeddings. To view the code easily, checkout the file at github

The animation on the website is made with threejs, and all the code is contained in the unfoldings.html, which you can also view on github.