Wow. My first thought was that the mirror was subtly uneven, distorting the reflections in a regular way. But watching the GIF cycle through a few times, it’s clear that it’s the tubes themselves that have been cut with a bias so as to make the cut ends look like diamonds one way and circles the other. I think the true cross-section of the tube is probably a four-sided super-ellipse or similar, but I’m having trouble picturing the cut end in my mind’s eye. And the overlapping diamonds/distinct circles one I can’t get my head around at all.
This was initially published in a special issue of Symmetry.
Anomalous Mirror Symmetry Generated by Optical Illusion by Kokichi Sugihara,
There are more ambiguous objects on the author’s website:
http://home.mims.meiji.ac.jp/~sugihara/ambiguousc/ambiguouscylindere.html
http://home.mims.meiji.ac.jp/~sugihara/invisibleobjects/invisibleobjectse.html
Oh that’s wonderfully awesome! It’s like having letter sculptures that read differently from different angles by the way you overlap and cut.
You would also notice that he never showed just 1, it would fall over. And now knowing the trick you can see the shadows and the bottom edges.
I especially like how Devin in the Make Anything video (the how-it-works video) at 1:17 calls the 3-D printed piece a hybrid squircle 
Oh hey I didn’t know that, I thought it was a word he made up on the spot! Thanks for linking to the wikipedia article, I think that’s really interesting. And this is something I love about the bbs here–I learn all kinds of stuff from people who take the time to post about something they know–thanks!
Can’t really call this video an explainer, but it does show the squircle from other angles:
They’re really easy to make - all you need is a cardboard tube:
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