Yeah, @roice713 the more I think about it the more this bothers me. And obviously I can't check them all, but I really don't see any other 10/10 edges. Is there an easy explanation for this?
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(I see one vertex that is 10,10,10,5; all other vertices I can count so far appear to be 5,10,5,10, as I think I should expect.)
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OK, up to 3 places where decagons share a face, but it's from two adjacent 5,10,10,10 vertices. Feels like an error; what am I missing? (Left hand side of the ring)
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Replying to @TheWheelMe @TilingBot
I think you're right! I hadn't looked close and thought this drawing had 3-fold symmetry but it doesn't. It's wacky and I'm kinda shocked it even seems to fit together. I suspect what is going on is that the quotient of the plane taken for this ring was in an unusual direction.
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Replying to @roice713 @TilingBot
Is it easy to explain what this means and why it would result in what I'm seeing?
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Replying to @TheWheelMe @TilingBot
The ring model takes a cut of the infinitely wide band model and bends it into a ring. In order to line up at the cut, the tiling has to repeat in the band. This usually means picking a very symmetrical orientation in the band model before cutting and bending to the ring. (1/n)
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But as long as the orientation in the band model is periodic, it could work, and there are surely some strange choices. I suspect what happened here is that the TilingBot's centering code caused the orientation to be unusual but workable. (2/n)
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aside: because of this periodicity requirement, one can't animate rotations in the ring model (at least not for the common case, maybe there are exceptions). It feels instructive to think about why. (3/n)
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I also guess I meant building one by cutting and pasting and scaling different rings with different color maps and different tilings on each one of them?
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It does seem like a rich artistic (and probably mathematical) idea to explore.
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I think there might be applications in either Teichmuller theory or in microlocal analysis. I want to call it a /mapping telescope of modular forms/hyperbolic symmetries/, except that you get one between pairs of latitude lines on -- something I don't understand.
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