I didn’t account for kerf. Also, there is a bit of overlap in lines in the vector that created a bit of an extra burn in one corner. I am guessing with a little bit of tinkering, someone could get the pieces to fit together a bit better.

Here is a PDF of the file I used (I tried to upload an SVG file, but I could not get it to load properly). I created a simple tray to hold the pieces together.

If you went and put the length on each length and the angle at each angle engraved before cutting I’ll bet That you might come up with a sizable percentage of the 536 solutions, I was trying to think of a way to color them by family or even number them that would get you back to the square but have not solved that puzzle

Thanks for these ideas! I will noodle them around my brain a bit.

I was thinking I could score the inside bottom of the tray with one solution, so at least we could get all the pieces back in the tray at the end of a play.

Of all things, we have a mathematician staying at our place tonight. We thought the puzzle would be a fun gift. Then, I thought, maybe he’d have good ideas for improving the project. (Always looking for ways to get folks to laser with me .)

I think that you will come up with a limited range if sizes for the sides and a number of sets that make 360-degrees at the angles That way if you put matching side to matching length side you will have a differently shaped object and by continuously doing so end up with the range of objects noted.

While I was thinking about it having a specific color for all the sides of the same length and another for each other, then if you could list the number where a combination of two numbers equals a third number and list all those sets etc you would have a very fun game for children that could teach serious math and geometry.

Cool puzzle! I would think the wood grain would help the solving.

You’re right, in that the wood grain helps orient the parts for the arrangement in which the parts were cut out, which helps. But not for the other 535 solutions.