The Origami Forum

Can someone guide me through 22.5 Design?
I know that the basic concept is making all points come out of 22.5 degree angles.
I have experimented with this and learnt to use it in some basic Fish and Kite Base models.
My question now is how to use it to create induvidual flaps?

I'm trying to learn this method as well. The best advice I can give is to practice arrangements of molecules until you can use them effectively.

I would also like to learn this if someone could teach us

I've been teaching myself, so I could probably teach you two as well (and anyone else who wants to learn). (:
So why not make this a topic where people can learn it?

I figure we can start with a relatively easy CP of mine, my Reindeer.

Reindeer CP by Baltorigamist, on Flickr
It would help if you were to fold this first, to study how the molecules I used work together to form the structure of the animal. (I'm willing to help you if you want it as well.)

Hmm, Thank you Balto!
I will try this next week if you dont mind.

designing with 22.5 takes time and dedication to truly understand it. you need to build up a library of different 22.5 molecules. in order to do that, you need to do a bit of free folding- try to discover molecules with many different and useful purposes. once you have you're library of molecules nice and expansive, you will be able to replace most irregular angled molecules with the 22.5 ones to varying degrees of accuracy.
here are some examples of how I used this method-
here's a scorpion varileg that I designed. I used treemaker for the basic structure (the resulting crease pattern closely resembled Robert Lang's scorpion varileg from insects II, so if you have that, you can compare the two crease patterns)

scorpion varileg cp by origamifreak64, on Flickr

and here's a flying grasshopper that I designed, this time I based the structure off of Robert Lang's flying grasshopper from insects II, so once again, if you have that, I strongly recommend comparing the two crease patterns to see how I directly replaced Lang's molecules to make it 22.5

Flying Grasshopper cp by origamifreak64, on Flickr
I hope this helps

great crease patterns!

I must admit I am not very skilled at 22.5° designing myself, especially when it comes to planning tthe design ahead.

I can freefold decent stuff using this folding method, but I really see I have a really big gap here in terms of knowledge and experience, but I have made a few relatively simple designs this way already. if you don't mind, here are the crease patterns:


this is a sketch of circle packing for a sea spider design, with boxpleated center though, and with some 30°angles, but my other ones are pure 22.5°technique:


This is a head of my hermit crab. now i see some of the color coding is wrong... crap...


this is an idea for a meganeura dragonfly. abdomen in the middle, wings in the corners, legs and antennae(or eyes) on the edges. the proportions are way off, but I may be able to improve it or use it for something else...


Octopus. yeah, I know, not very original... :/ it's an old design, if i can even call it that...


treefrog, with a very obvious reference point and structure. it was a freefold design and the cp was done "after the fact"
I have been perfecting the shaping for three years though, most of the unique characteristics of the model lie there.


crab from a bird base, it's one of my freefold designs, the cp was done "after the fact" as well


Mite, one of tthe few of these designs which was actually planned ahead as a CP. Yay!
I was super proud of this at the time, but I quickly started noticing how inefficient the design is.

Now, these three were planned ahead, but I'm not sure whether they fit the theme, because they're kinda boxpleated too, but just in case someone is interested:

tadpole


tadpole with hindlegs


froglet with a tail

I haven't folded any of the three models above yet...


tanystropheus. horrible. horrible horrible horrible. inefficient and the proportions are off too. no wonder it only exists as a single test fold. (this is another of the "after the fact" CPs, by the way, I just wanted to know what the model looks like structurally, and I was quite disappointed...


katydid with very long antennae, terrible. absolutely terrible.


hesperornis, CP planned ahead.


improved hesperornis, CP planned ahead


kuehneosuchus, my fold of it was horrible, but one nice person created a very stunning rendition of it, for which i'm very thankful:

the CP shows i didn't know what I was doing though, the rivers around the wings are complete nonsense, the rivers should go between the forelegs and the wings and between the wings and the hindlegs. i realized this years later, but because (like many of these, unfortunately) i created the CP in MS Paint, there was no esy way of correcting it.


this mouse is an oddball, i have actually drawn the diagrams before folding to see if I can follow the instructions and fold the model accordingly

my first attempt at a planned CP ever, Diplocaulus. the picture says "afterfold" because I unfolded the base to check some areas which I was uncertain about and "filled in the blanks" when the model was folded.


An improved version of the previous design


my third version of diplocaulus, completely different structure. the design was essencially a freefold too, only with pre-planned reference point (the long tred diagonal folds) found with treemaker. I am very proud of this design, it's got a perfectly crease-free body when folded, and it can even be folded without making the lengthwise diagonal crease. diagrams in progress.


this is supposed to be a simple fish.

I used to have uploaded a bear CP and a fish CP on my old flickr account where it was clear i didn't have a clue what i was doing, and i have already deleted the pictures, so this will have to do

I'd love to understand 22.5 designing, but I can't seem to understand it. It looks like one of the best techniques out there. I can't understand those "molecules." What exactly do they mean?

Molecules are areas of a CP bordered with axial creases. Trafitional pig base is from two "sawhorse molecules", fish, bird and frog base are from a varying number of "rabbit ear molecules" and so on. There are other types of molecules, like gusset molecules, but these are typical for odd-angle circle packing.

that explains a bit.

well i think you can imagine them as pieces of a puzzle that give you the desired result if you assemble them correctly. each molecule contains a section of a flap in each corner and sometimes even a part of a river.

Interesting. I'll keep update on whatever's up on this topic.

hopefully more people will contribute. this is something i desperately need to improve upon

22.5 degree designing is something I also am trying to figure out. I hope my tips help.
I totally agree with Nick on building up a collection of molecules. As your knowledge of molecules build, you will be able to build more complex bases.
I would start designing using the molecules you probably have experience with already, such as the fish base, bird base, and waterbomb base molecules. Even with these simple molecules, you can build some pretty decent bases. Robert Lang has a chapter in origami design secrets titled "tiling" which explains this concept further.
Practice is the best advice I can give though.

Here's a quick post because the first time I tried to do this it didn't work and got deleted.

Feel free to correct me on anything I've gotten wrong here.

MOLECULES

Molecules are shapes created by creases in a crease patterns with their vertexes corresponding to tips of flaps. Here is a simple crease patter, with the left side being only the molecules of the model (bird base).


Not all models are as simple as bird bases though! Here are some more molecules I've found to be most common and useful.



Using these, we can create a wide range of models. Remember, 45-45-90 molecules can be grouped together to form "group molecules" such as fish base, bird base, etc.

CIRCLE/POLYGON PACKING

Circle river packing can actually be used in 22.5˚ designs. Here is a method I use sometimes.

1: Design a model with circle river packing.
2: Shift the positions of the flaps slightly to meet up with 22.5 lines.
3: Fold!

But if we're working with circle river packing, we should be figuring out how much paper each flap uses up.

REFLECTION LINES

In a creases pattern, it might be useful to find out how much paper is taken up by each flap. To do this, I use what I call "reflection lines." These define the border of the flap, the very base of it. As a simple example, lets use bird base again.

For this example, we're going to try to find out how much paper the far right flap takes up. To do this using reflection lines, we start a line coming perpendicular from the edge of the paper (I'm mostly sure). When it goes over a crease, make it reflect over it. The creases that you use should be only the ones in the final flat folded model. Here's a picture of our progress.

Now, move the reflection line farther up the creases. But oh no! What happened? Our reflection line has switched, and now borders a different flap!

At the point where the reflection line changes is the edge of the flap. This image shows the paper taken up by two flaps.


Let's try this out on a more complex model. We're going to use a hummingbird I designed. It's a Marvelous Spatuletail. I put the long tail feather just off of the corners to get extra paper at the end of these flaps for the "spatulas." Here's the creases pattern.

And the same crease pattern with molecules highlighted.

Say I want to find out exactly how much paper my long tail flaps use up. Lets start a reflection line going.

But it's not going where we wanted! Let's move the line farther down the flap and try again.

Now we know exactly how much paper this flap uses up.

Here is a picture of all the flaps (on one side) shaded in and highlighted.

Additionally, we can also use this method to make rivers. Here the rivers are highlighted with a white overlay.

You may notice that some areas didn't work. This is probably because I messed up with the crease pattern. Use this to check if your creases pattern is correct before trying to fold it.

CONCLUSION

The things in this post is all by me. Feel free to critique, add on, are call me out wrong.
In my opinion, the best way to design 22.5 is to just try and fold a base. As you become more experienced, you can do this better. Enjoy folding!