I started watching this and was like ok, I'm with you, yep, you are deconstructing a cube, no problem, I am visua-WHAAAAAAAAAAAAAAT
Now I am going to have to try this if I have graph paper somewhere. I wonder if it would still work if you drew another line along the crease in the graph paper.
Had some graph paper so tried it. The illusion only works if you close one eye, and keep the paper evenly lit. Well lit with straight lines and a dark crease line appears either behind or on the cube’s surface but doesn’t effect the illusion of the cube snapping into place. Shading each side would probably enhance it.
But I can't find mine right now - I think I gave it to one of my sister's grandchildren when they last visited. I'll have to print and fold up a new one.
Here are the instructions and downloads if you want to make some - just print a single sheet on a color printer, cut out around the outline and fold into shape - the instructions are on the parts of the paper you cut away - very simple and kids enjoy making them - a bit of sticky tape or glue-stick on the tabs and base holds them together more securely, but you can manage without.
The head doesn't actually move - it's folded so that it's concave - we're not used to concave faces, so our brains interpret the changing view of the hollow face as a rotation of the model's head. Even when you know how it works, the illusion is still convincing - until you move far enough around that you start to see the other side of the paper.
I spent hours trying to get rid of them -- and -- they do not exist. It took while to prove that to myself.
There is an edge of sort there, for certain, but one of direction, not shade. Human eyes detect and enhance that, making them look whiter when they're not.