Dave, Sorry-not-sorry to bring up Penrose again. One of my favorite mathematical facts is that generalized Penrose tilings can be seen as a consequence of projecting a 5-dimensional lattice <https://arxiv.org/pdf/math-ph/0606028.pdf> into the plane, where this lattice can be imagined as a tiling of hyper-cubes. I am not sure this is helpful, but it is pretty cool. More to your goals:
two) I suspect not, but tell me more. Can you constrain the question? three) Perhaps showing my age, less than 8 years ago I had to prove for Dr. Starbird's class the theorem that there are only 5 regular Platonic solids. What was interesting about the proof is that no more than graph theory and algebra is needed. To some extent, it is what is beautiful about these really early theorems. Jon ps. I prefer Gmail for editing together a post.
- .... . -..-. . ...- --- .-.. ..- - .. --- -. -..-. .-- .. .-.. .-.. -..-. -... . -..-. .-.. .. ...- . -..-. ... - .-. . .- -- . -.. FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
