Penrose tiles with hidden tabs

This design is similar to an older printable of mine and you can read more about Penrose kites and darts there and on the Wikipedia page.

The main change is that the tabs that hold the tiles together are completely internal. They have a right isosceles triangle cross section and fit into corresponding holes. Because the tabs are suspended, they require support. I wasn't happy about using supports, but they are easy to remove after printing.

Unlike most of my designs, which use SVG imported from Inkscape, these were constructed entirely in Tinkercad. Here's the tinkercad link if you want to try to remix.

Getting these to fit well was harder than I expected even after making a proof of concept with the tabs. I eventually realized that:

• You need to maintain a uniform gap between tiles (just like in floor tiling). I added spacers around the sides for this.
• Once the spacing is determined, the dart scales slightly smaller than the kite. I determined about 97.5% but you can work out the geometry as an exercise if you want

Small differences compound in a tiling and it will tense and buckle if you're off by too much. I have provided two sizes of models: scaled to 10mm on the small tile, with a thickness of 3mm and scaled to 12mm with a thickness of 3.6mm. The larger ones are easier to work with, but both fit together to make liftable tilings.

I have only changed the scale, so you can try other sizes. Keep the proportions the same so the overhangs print at 45 degrees. You might get away with slightly thinner tiles, however. I have not tried.

Because the tabs are internal, the tiling can be displayed either top or bottom without any jigsaw fittings showing as in my older model.