The idea of solving polycube problems in higher dimensions is interesting, though I haven’t thought much about it myself. I’m not sure how hard it would be to add another dimension to my solver. Probably doable, though graphical I/O would be challenging, and it would be harder to verify correctness just because 4 dimensional things are hard to think about.

I just did a web search for N dimensional polycubes. Although I did see a few related results, I don’t immediately see an N-dimensional polycube puzzle solver.

Your box sounds small enough that you may not need the fastest solver. You might just try a generic DLX solver, coupled with an N-dimensional rotation utility to generate the rows of the matrix.

Good Luck!

]]>This is realy great job. I have now solved the same task with only a 4-dimensional domain. We need to find the exact number of coatings 2x3x3x5 box by 5-cell hypercubes (design begins with the initial cube, joined by another cube in the direction of one of the measurements, and then the operation is repeated for the remaining measurements, with new cube is always attached to the previous one). Maybe you have a reference to the decision of a similar problem. Sorry for my English. ]]>

I’m not sure what you are asking.

Are you looking for a script to convert a set of solutions into some other format suitable for yEd?

Or are you looking for a mechanism to sort the set of solutions into a desirable tree of solutions? I think most any solver (including mine) outputs solutions following a “tree”, but the solution set can obviously be organized into many different trees. Are you looking to reorganize the solutions into a “better” tree? What measure do you apply to distinguish a “good” tree from a “bad” one?

–Matt

]]>I have been using yEd graphing SW (http://www.yworks.com/en/products_yed_helpresources.html)

to visualize SOMA solutions(good pics towards the end of post).

http://www.mathisfunforum.com/viewtopic.php?id=21536

These graphs are beautiful but it involves “steps” of getting the solutions into a format acceptable to yEd and this is diluting the “mathiness” that I think can lead to some more interesting thoughts about these sorts of puzzles.

I am working with this code in Python Spyder:

http://www.cs.mcgill.ca/~aassaf9/python/algorithm_x.html

as a starting point to solve, classify and graph a some simple tiling puzzles.

Thanks for your exhaustive and well documented post.

Best regards,

Edward Vogel

The Envirostone that I was unable to blow/wash off the surface of the stone the day I put it in, did eventually weather off on it’s own. I have had to poison a few ant holes each season. And I have had just a few weeds grow through it in the line between the flagstone patio and the concrete patio (where the weed block ends), so if you use this product, I think putting weed block under it is probably a good idea.

That beautiful stain job didn’t last a year on the decking. I think I put the stain on too soon — the wood had too much oil in it and the stain didn’t adhere. I power-washed the deck and put down two coats of the same Cabot transparent cedar stain again the next spring. It’s been over a year since this second application and it still looks good.

My only regret is using cedar. Within two weeks of the finish photos above, we had a nasty hail storm which dinged the heck out of the deck. We have had at least 6 hail storms in the last two years. I had seriously considered putting in ipe for the decking and rails, but eventually decided on the cheaper cedar. I think the ipe hardwood would have withstood the hail much better than the cedar I put in. All-and-all, the deck still looks quite nice (despite the dings).

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