Acyclic Monotiles

Everyone in the math community is all excited about the acylic monotiles that were discovered.

I don’t have much to add, but I did recreate it in Solidworks and laser cut it out:

I created a hexagon, and subdivided with construction lines, and saved that as a block.

I then inserted 5 more of these blocks:

Note that I think the ‘center’ doesn’t actually need to be in the center, and it will still tile, for more interesting shapes:

Then I draw the shape I wanted, shown in orange, and saved this as a block.

Then I created TWO new blocks. In the first block, I inserted that orange outline block, and drew on the shirt pattern. Then in the second block, I insert the same block, but mirrored it and drew on the back of the t-shirt.

Then I could insert a whole bunch of the two blocks, and manually arrange them together like a jigsaw, snapping edges together.

Then saved it as a DXF file and imported it into Inkscape, manually moving the cut lines and score lines to separate layers and giving them separate colors. I also had to manually delete overlapping lines. I’m not aware of a better approach.

Then cut on my laser cutter: