The Origami Forum

Are there any advantages that hex pleating has over box pleating? If so, are they worth it? I have read that packing hexagons is more efficient than packing squares, but I dont know if that would necessairly transfer to origami.

Hexagon packing is indeed more efficient than square packing (at least if my memory serves), but the difference isn't quite as much as you might imagine. There's also the fact that triangle grids, pretty much by definition, don't fit in squares very well at all, which means that hex-pleating isn't very practical.

I second everything Balto said, it might be more efficient than pure square packing bp, but with pythagorean stretches bp becomes just as efficient if not more efficient than hp. The only practical application I can think of that hp has over bp would be for incorporating triangular patterns/textures into a larger design (eg, a turtle shell).

I see. So, I could make a model with a general square gid and use hex pleating only to give texture, right? Also, if I plan on making something “circle-like”, would box pleating still be better?

This is funny. I named my new tortoise "Nameless", mostly because I can't yet confidently determine if it's a he or a she. I like the name "Nameless", though, mostly for the irony. I got Nameless a few moths ago and he/she has already picked up over 200 grams, a third of his/her weight.

Yeah, I also chose the name Nameless for the irony. I generally prefer Nemo, but I tend to be confused with the fish, rather than the captain, which is the guy that inspired me not to choose a name for my social media accounts.

If you want the efficiency of circle packing but without actual circle packing, i'd say to do bp with pythas. i've never tried incorporating 60 degree textures into bp but i'd assume it would be pretty difficult to get it to work nicely. Most textures on bp models can be achieved with regular 45 degree angles plus shaping (think like ryujin scales)