3D models of the unfoldings of the hypercube?

Question

There are (apparently) 261 distinct unfoldings of the 4D hypercube, a.k.a., the tesseract, into 3D.¹ These unfoldings (or "nets") are analogous to the 11 unfoldings of the 3D cube into the plane.² Usually only one hypercube unfolding is illustrated,

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          ^{(Image from this link.)}

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the one made famous in Salvador Dali's painting Corpus Hypercubus. My question is:

Q. Has anyone made models/images of the 261 unfoldings as solid objects in $\mathbb{R}^3$?

(If not, I might do so myself.) I previously asked this question on MathOverflow.

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¹Peter Terney, "Unfolding the Tesseract." Journal of Recreational Mathematics, Vol. 17(1), 1984-85.

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²

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Answer 1

This question has been asked and answered on MathOverflow. I have replicated the accepted answer by Mark McClure below.

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.