Earlier this year I wrote a couple blog posts about reverse engineering Sugihara’s impossible cylinder illusion. I then wrote it up more formally, and it has appeared in Math Horizons (pdf).
The example I gave on my blog and in the article was a cylinder that looked like a circular cylinder but like a square cylinder in the mirror. You can download a printable pdf template to make your own, and you can watch this video that I made.
Today I designed two more impossible cylinders. The first looks like a square cylinder and like a triangular cylinder in the mirror. Download a printable pdf template to make your own.
I also designed one that looks like a heart-shaped cylinder and like a diamond-shaped cylinder in the mirror. (The spade/club one is an exercise for the reader.) Here’s a template to make your own.
Update: I just created another cylinder. I’m not as pleased with this one. The shape of the cylinder is complicated enough that it is difficult to get it to look right. Here’s my best attempt at a star/moon cylinder. (Pdf template.)