PolyCross

[Robotguy]

It's not really a model, but I've been using Small Stella for visualization as I construct a new type of crossword that is played on the surface of regular polyhedra.





http://www.youtube.com/watch?v=c8Yt9iJUhuQ


Eventually this will be either magnetic tiles that enable the player to construct a polyhedron (see prototypes above), or a polyhedron with dry-erase in the appropriate locations. For now I unfolded a truncated icosahedron and created a version that has a dozen 5-letter words and is easy to print. This will require either some good 3d visualization skills, or some construction with scissors and tape. I would appreciate any feedback.

Please don't post the solution. The puzzle is pretty much self-verifying, but if anyone wants me to check answers, please PM me. Oh, as you may guess, the solution shown in the above examples is not the same as the puzzle below.

Click here for the puzzle------>PolyCross

P.S. I also have an idea about playing Sudoku on a rhombicosidodecahedron.

[Ulrich]

Nice idea! With less symmetric shapes it can be extended to any complexity. But that would call for an electronic version.

Ulrich

[Robotguy]

Just an update, still working on this. I tried tiles with magnets but was disappointed with the results, so I am updating the snap-together tiles and should have my next prototype soon. I upgraded to Great Stella and am still discovering the new features. My favorite so far is animated GIFs:
https://dl.dropboxusercontent.com/u/302 ... zzles.html

[Robotguy]

Another update (Yes, I've been working on this on and off for many years). I finally gave up and fixed the dihedral angles so these tiles can really only make a truncated icosahedron. Each edge has 2 small magnets, North and South, so they go together with a very satisfying SNAP. I have created 5 different puzzles; the extra tiles you see are the ones needed to make other puzzles. Everyone keeps telling me I should market or sell these but that sounds like a lot of work...

Poly.jpg (112.83 KiB) Viewed 48809 times

[robertw]

Interesting idea. Do the words always go clockwise around each number?

[Robotguy]

I tend to dip in and out of this project so 3 years for a reply is about par for me

To answer your question, the solution works in both clockwise and anti clockwise directions as long as you’re consistent. I didn’t realize this at first and just assumed (I know, I know) that everyone would build clockwise, but then a coworker was playing with it and built it anticlockwise and it worked.