ConwayLife.com

These tiles are made by gluing small pieces of cut card stock into layers to make 3D boundaries to force correct placement as well as to hold them together. I use a frame (shown) to line up the layers for gluing. They're not hard to fit together as long as the tabs are aligned and don't get bent, and they hold very well once placed. The assembled part shown reliably survives a drop from table to floor. You have to fit light and dark bumps together with the light bump on top. They are admittedly delicate and will break if forced (trying to fit light to light or dark to dark). One nice thing about them is that they are symmetric when flipped over. The white bumps are always on top and in the same position.

Tile thickness is about 1.5mm and bump thickness is about 1/3 of that (0.5mm). I could make these bigger, but I kept the small side at 1cm to push the limits. I plan to use a similar approach for a new set of still life tiles.

Here's a view showing edges: I assume this could be made more easily with a 3D printer, but I'm not sure if overhang is an issue. I am also not sure how you'd color the bumps, which is not in itself necessary but helps avoid mistakes.

I made a total of 13 kites and 12 darts this way. Sometimes they fit very well, but they're unreliable. If you squash the tab a little it just continues to get worse. Still, this is somewhat liftable: I have some other ideas that would not hide the tabs and I might use them for still life tiles, but I think for Penrose tiles, it's a feature not a bug that you can't see the boundary constraint other than edge length.

I could increase the size of the tiles. I could also increase the size of the tabs. Those are 3mm diameter half-circles. I think I could increase them to 6mm. If I used 8 layers (3 for each tab and hole and 2 for top and bottom) then they wouldn't bend as easily.

Once I'm happy with Penrose tiles I'll extend the lesson to still life tiles.