A puzzle that tiles infinitely across both sides, based on the Klein Bottle(n-e-r-v-o-u-s.com) |
A puzzle that tiles infinitely across both sides, based on the Klein Bottle(n-e-r-v-o-u-s.com) |
http://anathem.wikia.com/wiki/Teglon
or
https://en.wikipedia.org/wiki/Penrose_tiling
I would love to have a Penrose tiling puzzle set.
I reverse-engineered the tiles in OpenSCAD. Let me know and I'll upload them.
https://hyperallergic.com/416579/engare-game-islamic-design/
I might just be bad at it though. On the other hand, the challenge is part of the appeal to me.
> Multiple infinity puzzles can be combined to create a larger continuous puzzle. The image above shows some of the creative combinations possible with two infinity puzzles of different colors ($75, for two).
here is the image from the quote: https://i2.wp.com/n-e-r-v-o-u-s.com/blog/wp-content/uploads/...
EDIT: FWIW torus puzzles are definitely not a new thing - I had this one as a kid: http://img.tradera.net/images/096/270662096_95a37033-d8f9-4c...
Edit: You can even put in some liquid (the “hose” continues through the crossing). The fun part is getting it out again :)
Every closed surface comes from a symmetry of the sphere, the Euclidean plane, or the hyperbolic plane. For instance, you can get a (flat) torus by taking the Euclidean plane and taking all translations that shift the plane in the x and y directions by integer amounts, where we consider two points to be "the same" if they are translates of each other. So, if you take a path horizontally, you periodically return to "the same" point every unit distance. This is the Asteroids geometry.
The Klein bottle can be obtained by the symmetry generated by two transformations: (1) a vertical translation by 1 unit and (2) a horizontal translation by 1 unit followed by a vertical flip.
The wooden puzzles are from tiling the plane in a way that respects one of these symmetries, and then taking just enough puzzle pieces to cover the fundamental domain. For the Klein bottle, all this together means that in one direction you can take off a piece and put it down on the other side in the same orientation, and in the other direction you have to flip the piece over.
I do find it a little annoying that the internet has made it common to price based on the people who will pay the most for things. It is still just cardboard. Just because it's an interesting idea doesn't necessarily make 236 pieces of cardboard worth $120.
To counter your point, this is like paying $120 for chick-fil-a nuggets instead of $5 for McDonald's nuggets. It's still just cardboard. It's slightly better made cardboard with maybe a little extra care, but it's just cardboard.
Anyway, "puzzle" is now available at https://drive.google.com/file/d/1KYDTZ2AVWQfWCSACUvfl5gAIHzA...
If I counted correctly, you should be able to make a roughly rectangular shape out of the provided pieces. (Even if I miscalculated, I think they make a good exploration toy for the P2 tiling anyway.)
Glad he is not famous only for that book. As fine as it is.
