Einstein Tiles + Magnets

Known as The Hat or Einstein, this 13-sided shape can be endlessly tiled without repeating its pattern. I found that it works as an unsolvable puzzle when I added a magnet and arranged the pieces on a steel surface. The magnet keeps the pieces in place as you nudge them together. Suitable steel surfaces include baking pans and sheets, pizza pans and steel plates. Aluminum won't work, nor will stainless steel: they're not attractive to magnets. Carbon steel is a sure bet. Alloy steel might work, depending on the metal used to produce the alloy.

You'll quickly find that mating the Einsteins is a bit tricky. They fit together easily but some of the patterns produce shapes that will not allow further development. When that happens, undo your recent moves and modify the pattern.

The magnets I used measure 5.97mm diameter by 1.65mm high. They friction fit in this design. (The magnets I used were listed as 6mm x 2mm; apparently they shrink during processing, like hamburgers.) You can use cheap craft/refrigerator magnets, but you'll get better holding power by shopping for good-quality neodymium magnets. Print one piece to see if your magnets are a good fit. If not, measure your magnets with a micrometer and scale the print in your slicer. (To scale, divide your measurement by the design measurement and use that as a multiplier.) Match the height of your Einstein to the height of your magnet: You'll use some of the pieces upside down and you want equal attraction on both orientations.

For those who don't want to bother with magnets I've included a solid version: no magnet hole. They're usable though the lack of a magnet makes them a challenge to arrange.