Learning 22.5 Part 2

 The next design I attempted was Saku Saku's Kelbi (the equivalent(?) of a deer from the game Monster Hunter).

I spent a while trying to figure out the references by hand, and eventually gave up. I asked on the Origami Dan discord, and was told the reference was 1+1+1+ √2. I had no idea what this meant. Turns out cot(22.5º) = 1 + √2. Years of math competitions and I'm still a beginner at geometry evidently.

I still didn't know what to do with this information (short of using some awkward reference from reference finder), until I was told that there was a very useful reference finder on Satoshi Kamiya's website perfect for references of the form a+ b√2: https://www.folders.jp/reference/reference.html

I inputted 3+√2 and got this:

From here it was pretty straightforward. This is all I drew up in ORIPA:

Here are some progress pictures:

Getting the base to resemble the final Kelbi was not too hard from here. It's a really nice design.

A couple days later I taught it to a chemistry friend over a zoom call, so I have another now. I skipped some folds in the head which led to longer antlers(?):

I also attempted Kaede Nakamura's Tiger. The CP is here. Since tan(22.5º) = √2 - 1, the reference ends up being 1 +√2:

You can use the aforementioned reference finder to get a reference for this: https://www.folders.jp/reference/reference.html

The collapse was pretty straightforward now that I actually understood what was going on with the references.

I'm not nearly good enough at shaping to turn this into the finished tiger, but it is nice to know that I can at least figure out the references now.

Learning 22.5 Part 1

I recently decided to put more effort into learning how to fold 22.5 designs. I think this post needs a pretty lengthy preface about why I made this decision, and why I think it's so important, but I'm too tired to write it right now. Maybe later.

In general though, I think 22.5 is more elegant than box pleating for most subjects, and at some point I feel like 22.5 will become far less popular than it deserves.

In the past, much of my trouble with 22.5 cps was finding reference points. Once I have the precreasing done, I can typically figure out the rest.

The first design I attempted was Obelisk's Nazgul. The CP can be found here.

I first redrew some of the important parts of the CP in ORIPA. I've included some of what I figured out below in case it helps anyone (seems like the kind of thing I would have appreciated years ago).

Then I collapsed the base, which wasn't too much trouble (but a little tricky in a few places. There are a lot of extra folds in the original CP which come about from moving flaps into place which I have always had trouble interpreting.

The next design I attempted was Kaede Nakamura's Spinosaurus. Here's a link to his website. I remember looking at this pattern a long time ago (around 2016-17?) and having no idea how to even start precreasing it. Somehow this time, the references just clicked for me and I figured them out within a minute or so. I drew the reference out the reference I used in Inkscape (I was interested in learning how to diagram, but unfortunately Inkscape is extremely slow on mac so I guess I won't be diagramming):

This is the portion of the pattern that I drew out in ORIPA:

I folded the base using 9 inch Kami:

I didn't find a great folding sequence for all of it, but I do remember finding something elegant for the folding the front half. At any rate  I was able to collapse it relatively cleanly. I didn't bother shaping it, because getting from this base to the finished design looks extremely wonky (also 9 inch Kami).

The last CP I attempted was Kaede Nakamura's Carnotaurus. Once again here's a link to his website. The reference was the same as the Spinosaurus, and I didn't bother drawing it out in ORIPA. I've always wanted to make this design (I really like the authors fold) but had no idea how to find the reference.

The base was relatively straightforward, but the actual shaping was extremely confusing. Kaede Nakamura (and probably most 22.5 designers) are clearly extremely talented.

I'm no good at point splits so I did them on the left side arms (the side facing the camera, although you can't see them because of the angle), but I didn't even bother on the right side arms.