Hi there,
How would one go about designing models of 22.5 degrees? I heard it doesn't use much math, and the reference points are easy to find, which results in a nice folding sequence. So what is the process? If someone with experience in this technique could reply, that would be great!
thanks
Justin
Given that I work with BP more than 22.5 in general, I'm not sure how much help I can offer. But everything I know about 22.5 I learned via experimentation. Fold a half-bird, half-frog base, make a few point splits, add a few other molecules if you want. Make an offset waterbomb at 1:sqrt2 and petal-fold. Basically, don't be afraid to try something different.
It's all in the tiling. Simply constrain yourself to octagons, etc. or just improvise.
References--that's the one thing I have trouble with. I just find a "simple" proportion (e.g. 4(1+sqrt2) : 3 : 2sqrt2)and convert the measurements to a decimal. Then I plug the result into ReferenceFinder. I'm sure there's a simpler way, but my method works.
That's just a hypothetical proportion, but 4(1+sqrt2) is 4+4sqrt2, so the sqrt of 2 times 4 plus another 4. That's the length of the first distance (10.18-ish, give or take a little--I'm going mentally). The second distance is 3 units, and the third is twice the square root of 2, about 2.83. Now that I realize it, that's close to a 16x16 grid, but the respective marks on the paper would be at 10.18 units from the edge (or whatever the actual distance is) and 13.18 units from the same edge, with 2.83 units left over.
This is really difficult to explain, at least for me. Maybe someone else can tell you better, because I'm a horrible teacher. lol
as Balt said, that is simply a hypothetical proportion. In some of Brian's cp's, he uses 2sqrt2 or something similar as a reference, for example.
sqrt = square root
4(1+sqrt2):3:2sqrt2
lets do the distributive property, now we have:
4+4sqrt2 :3: 2sqrt2
solve 2sqrt2 first. square root of 2 is about 1.415, and 1.415 x 2 = 2.83
now we have 4+4sqrt2 :3: 2.83
to solve 4+4sqrt2, you'll take the square root of 2 first, and once again, thats 1.415
multiply that by 4. you'll get 5.66
now add 4 to that, and you'll get 9.66
the proportion now is: 9.66:3:2.83 (much easier to read)
so essentially what this is telling you is the location of a point on the paper - a reference point. in this case, it would be at 9.66 units from the edge and another at 12.66 units from the same edge, with 2.83 units left over.
As I stated earlier, it's really all about experimentation. There's an old model of mine that's currently unpublished, a swordsman, that is purely 22.5 with a few pleated folds. It was improvised, no previous planning, etc.
Again, it takes time. Insects are tricky to do in 22.5 because its usually difficult to fine-tune flap length like in circle packing.
Hi cowburger13,
I would say from experience that 22.5 degree design is a little trickier to plan from a cp than bp, but if you have an idea of what you want to make, you can create a "rough" version of a base in your mind. Personally, I'm not a fan of symmetrical 22.5 degree bases like fish, frog, or bird bases as starting point- i think they limit creativity. Instead, I start like this- I draw a rough circle packing for the design I want to make- and design off of a point of a square, not an edge. Then, start collapsing with the smallest/ shortest points at one corner and expand outward to the larger ones. Thanks just how I do it- it works for me.
Overall, I'd say just start playing around with asymetrical bases, and you'll figure something out. Good luck!
If someone with experience in this technique could reply, that would be great! 
