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Tamatebako notes
Nov. 12th, 2009 12:53 pmHave resumed fiddling around with the tamatebako pattern. More specifically, I've been trying to find a flat triangular hinge for the cuboctahedral variant-- Tomoko Fuse has a 3-pocket equilateral triangle in one of her books on modular polyhedra, but there isn't enough internal friction to hold the flaps in place so they pretty much have to be glued anyway, which misses the point.
As an alternative, there're Lew Rozelle's "three-sided bases", but those have their own problems. Because they're pyramidal, the final shape would end up just being a larger cube, albeit more complexly patterned. Their closure method is rather bulky, requiring thin paper with a much thicker internal insert to provide internal structure; the smallest thin-paper squares I have on hand are 3".
And then there's the question of relative paper sizes, although the logistics actually simplify quite a bit inm practice. Starting with an N-sized square for the tamatebako face, the face flap is N/3. This theoretically dictates a 2N/3 square to fold a simple pyramid (reasonably straightforward)-- and for a complex pyramid, a 2N/(sqrt 3) square (somewhat less straightforward; ~(1.155)N ). However, on my usual scale where N = 3.5" or 3", an N-sized square for the complex pyramids is a pretty good fit.
OTOH, the complex pyramids are obviously more complex to fold (not too much-- mostly just a matter of an extra blintz step at the beginning), but while it's not too difficult to measure and cut 2" squares for simple pyramids with N = 3" , it's a bit more fiddly to measure and cut 2-1/3" squares for N = 3.5".
...though if I have to measure and cut 2" squares anyway, it's not that much more of a task to measure and cut 3" squares while I'm at it.
As an alternative, there're Lew Rozelle's "three-sided bases", but those have their own problems. Because they're pyramidal, the final shape would end up just being a larger cube, albeit more complexly patterned. Their closure method is rather bulky, requiring thin paper with a much thicker internal insert to provide internal structure; the smallest thin-paper squares I have on hand are 3".
And then there's the question of relative paper sizes, although the logistics actually simplify quite a bit inm practice. Starting with an N-sized square for the tamatebako face, the face flap is N/3. This theoretically dictates a 2N/3 square to fold a simple pyramid (reasonably straightforward)-- and for a complex pyramid, a 2N/(sqrt 3) square (somewhat less straightforward; ~(1.155)N ). However, on my usual scale where N = 3.5" or 3", an N-sized square for the complex pyramids is a pretty good fit.
OTOH, the complex pyramids are obviously more complex to fold (not too much-- mostly just a matter of an extra blintz step at the beginning), but while it's not too difficult to measure and cut 2" squares for simple pyramids with N = 3" , it's a bit more fiddly to measure and cut 2-1/3" squares for N = 3.5".
...though if I have to measure and cut 2" squares anyway, it's not that much more of a task to measure and cut 3" squares while I'm at it.