There are many tube-like accordion folds. If any of them permit any bending, they could be bent into a ring that would almost certainly permit the toroidal rotation that Jim remembers from that cubical toy. (I think we may have one.) On Wed, May 28, 2014 at 2:17 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Other flat tori would be interesting, too, but especially the other maximally symmetric one, the hexagonal torus. Which has a triangulation by N equilateral triangles, 6/vertex, at least for any N = 2 x 7^k or N = 6 x 7^k, k >= 0.
--Dan
On May 27, 2014, at 8:50 PM, James Propp <jamespropp@gmail.com> wrote:
Where can I learn about, and see pictures of, polyhedral surfaces in R^3 that are locally flat (the angles at each vertex add up to 360 degrees) and have the global topology of R^2/Z^2?
More specifically and concretely, how can I crease and fold a square sheet of paper [0,1]x[0,1] so that I can actually glue (t,0) to (t,1) and (0,t) to (1,t) for every t in [0,1]?
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