Post #2870357
2026-04-16 12:53 UTC
@matt_zucker@mastodon.social
So to test my understanding, in order to make them tileable you have to define - for one tile - a surface where all three or four edges loop back on each other (torus geometry for four edges). And for multiple patterns you need multiple surfaces that still all share the same single edge.
Now, it should matter which way they're flipped. Is there more than one way to arrange the flips of the common edges? Or there is only the one?
Replies (1)
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@matt_zucker@mastodon.social 2026-04-16 12:58
@jannem@fosstodon.org not quite torus geometry. A torus is a manifold (https://en.wikipedia.org/wiki/Manifold) and my folded-square-thing is most definitely not. Torus would be the same as the "Pac-Man" periodic boundary conditions I alluded to earlier. That gives two distinct edges that loosely correspond to the "equator" and "prime meridian" of the torus. Yes for multiple patterns you need to have multiple sheets sharing the same edge. (cont'd...)