Archimede's Stomachion

Free Laser Designs
#1

Archimede’s Stomachion has 536 distinct solutions. However, just finding one solution was a challenge. There is a free svg download in Wikimedia Commons.

IMG_0772
IMG_0772.jpeg2230×1260 688 KB

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.

Ostomachion.pdf (43.3 KB)

36 Likes
#2

Very cool! (I never have the patience to figure them out, but I usually wind up with a crane or something out of the deal.)

4 Likes
#3

Thank you for sharing

3 Likes
#4

Thanks. Very nicely done.

3 Likes
#5

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

3 Likes
#6

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 :upside_down_face:.)

7 Likes
#7

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.

1 Like
#8

Rad!! Thank you!

2 Likes
#9

This is awesome! I tweaked it slightly to so a solution is scored into the base, sharing in case it’s useful. OstomachionScore.pdf (48.8 KB)

My son is now agonizing over this puzzle. It’s hard! No wonder they had to write software to ‘brute force’ find all the solutions!

6 Likes
#10

Right? It took us about 30 minutes to figure out one solution looking at the solution. Thanks for the updated file! You rock!

4 Likes
#11

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

3 Likes
#12

On one or just a couple of solutions. no help ay all on most.

3 Likes
#13

Very nice! Thank you!

2 Likes
#14

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. :slight_smile:

3 Likes