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DominikPeters
Videos showing rotations: https://www.youtube.com/watch?v=KtA6u1HIqbg (Garage roof) https://www.youtube.com/watch?v=oWfFco7K9v8 (cylinders)
kurthr
And this guy shows how you can 3D print the squicular design by varying the height of the edges (arch up on 2 sides and arch down between the other 2)... it only works well at ~45deg angle.

https://youtu.be/SKpOKXAVjGo

Jeff_Brown
That first video is so much more helpful than the second. Funny how you (or I at least) can see the thing rotate and still have no idea what it looks like.

An interactive experience would be more illuminating. What's some good software that'll let me rotate the 3d model?

inimino
You can approximate this by dragging the scrubber on the youtube video back and forth while the object is being rotated. When it's about half-way rotated, then it all makes sense.
samplatt
Short version - both the camera angle and the angle of reflection from the mirror are producing forced-perspective illusions.

The object topology is not accurately shown in the camera perspective OR the mirror.

This took me way too long >_>

whoisburbansky
The phrase “forced perspective” really keys into why this works, at least for me. Doesn’t take away the magic of seeing it in action, but it does help with some of the “how in the world?”-ness of it.
DubiousPusher
This is amazing but my brain is not happy about this.
tiahura
Wait. What?

This is like the Monty Hall problem to my brain.

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hn_throwaway_99
I love illusions like this because to me they are a reminder of how absolutely amazing the human visual system is. Far from exposing "flaws" in human vision, I see them as showing how good human vision is at interpreting 2D data as a 3D scene. Our brains assume the 3D scene as what we are statistically most likely to encounter in the real world, but when you come up with a statistically highly unlikely 3D object that projects onto the same 2D space as the more common object, our brains assume the more common version.
zomglings
Amazing! After watching the second video about the cylinders (https://www.youtube.com/watch?v=oWfFco7K9v8), I still couldn't understand the illusion. Would have loved a demonstration where he rotated them also along the axis parallel to the base of the mirror.
slver
I was hoping this is some new OOP technique... "ambiguous objects". The term awaits a consultant to make it shiny and attractive.
gryz
It would be interesting to observe the effect myself but bringing the cellphone with a picture to the mirror... Not possible?