## Introduction: K2 - Complex Modular Origami Sculpture - No Glue

Hi there :)

For those of you unfamiliar with the art of Origami, these are probably the models on this webside with the highest skill/price ratio :) They cost you nothing except time and a few sheets of paper...

Aaaaand, this piece of art is completely biodegradable :)

Here's a little bit of complex paper art for you to have some fun with. The assembly is very similar to Thomas Hulls 5 Intersecting Tetrahedra (there's an instructable for it), I would recommend folding that first if you haven't yet.

The original diagrams are in the OrigamiUSA issue of 2002 ( I think).

This is a complex rendition of a Great Stellated Dodecahedron, with 60 pieces of paper folded into 20 triangles comprising 5 tetrahedra.

Oh and if I win the Epilog laser cutter with this instructable, I will use it to laser a labyrinth into a medical textbook of mine and put a ball bearing inside the book that one can roll around like a maze... I've been wanting to do this for a while, but I haven't gotten the opportunity yet, so if you're feeling nice then vote for me :) I might even post an instructable about it if I get it done...

What you will need:

10 squares of paper

CDO (Kinda like OCD, except the letters are in alphabetical order. As they should be...)

Ok lets get started!

## Step 1: The Paper

The paper dimensions we are going for is 1x6 rectangles, so cut your 10 squares into 6 equal strips.

There are several colouring schemes which work well for this model, I used one in which each tetrahedra was a single colour (12 pieces of each colour, 5 different colours), but you can make each triangle the same colour (3 pieces of each colour, therefore 20 different colours/patterns).

A random or chaotic pattern contrasts nicely with the sharp lines of this model and works well too.

Don't skimp on the paper. You are going to spend quite some time folding this, the extra 5 minutes you take to print out a nice pattern will make a world of difference when the model is finished.

## Step 2: The Folding Begins!

This model takes a while to fold.

Each piece takes about 6 or 7 minutes, and there's 60 of them, so you're talking 6 or 7 hours just for the folding, and another 2 or 3 to put it all together.

There are no shortcuts to anywhere worth going!

Ok turn your paper sideways (if you are using coloured paper, start with the white side up) and fold the bottom right corner up. do the same with the bottom left corner.

This is only a guideline crease, so don't crease too heavily.

## Step 3:

Fold the bottom corner and line up to the crease you have just made, and only crease on the part of the fold that touches the short edge (this is another guideline fold).

Do the same on the other side.

## Step 4:

Fold up on the crease you have just made, and fold across to the other crease on the other side of the paper.

You will notice that this divides the paper into 2 UNEQUAL halves.

## Step 5:

Fold the paper along this crease you have made. This is difficult, try to do it accurately.

I find it helps to fold a little bit on both sides, then to tackle the middle.

## Step 6:

Unfold this, and fold the edges to the middle. Unfold all this.

## Step 7:

Fold the bottom left corner between the "middle" fold and the fold you have just made (this is on the smaller of the 2 halves.

Fold again to the middle.

Fold the top left corner down to the middle.

Repeat on the right hand side.

## Step 8:

Unfold all this and fold the edges to the middle again.

## Step 9:

Sink the top left corner along the existing folds. Flatten.

## Step 10:

Sink the bottom left corner in. The folds are there at the back, but you will have to make them in the front. I have turned the model over and indicated the line.

Flatten.

## Step 11:

Turn the little flap over it's bracket and flatten. Unfold and hide under the opposite reverse fold.

## Step 12:

Fold the right top corner down along the existing crease.

Fold the bottom right corner up along both of the existing creases. The creases are present at the back, these folds are to crease the front of the paper.

Unfold all this, and flatten the whole piece again along the midline to make sure it's flat (don't worry about flattening the left hand corner, it's difficult and unnecessary).

## Step 13:

Success!

Fold another 59.

Tuck the double flap of one model into the sunken fold of another (flap visible for clarity, should be hidden).

Pinch to lock, and fold the other flap into the other pocket.

Stick 3 together into a triangle.

## Step 14:

Fold another triangle, and lock it into the first one. Notice that the 2 small edges are facing each other.

The assemble of this model is not hard, if you concentrate during these first couple of steps.

Notice the EXACT position that the 2 triangles are in.

## Step 15:

Add a 3rd triangle, notice the way the 3 interact. The small edge of each triangle has to face toward the corresponding face of the tetrahedra, which means that the 3 small faces are all touching where the triangles intersect.

They go over one another in a clockwise fashion, copy this exactly.

Wrap sticky tape around this corner where the 3 triangles meet to hold it in place.

## Step 16:

Add a fourth triangle at the bottom, keeping the same configuration.

Remember: small edge on the face of the tetrahedron, the 3 small edges touching one another where the triangles meet.

Wrap sticky tape around the 4 corners to make sure the tetrahedron doesn't fall apart.

## Step 17:

From now on, the assembly is identical to that of 5 intersecting tetrahedra.

Add an extra triangle as shown, and assemble another tetrahedra intersecting the first one. I have uploaded the instructions for the assembly of 5IT to make life easier :)

## Step 18:

Add a third tetrahedron :)

## Step 19:

Add a fourth. I found this one to be the hardest.

## Step 20:

The 5th and final tetrahedron. This one is easy, you can see where each arm is supposed to go. Good work. Go get some fresh air. :)

Now.

You.

Really.

Have.

Folded.

Something.

Spectacular!

I'm scared

the measures are in cm or inches?

i

Seeing as either one would have the same w:h ratio, 6:1, feel free to use either. The only difference will that inches will produce a larger end model, and vice-versa for cm.

Hell, you could do 1x6m and it would still work, it would just be on and unmanageable scale.

Thanks for posting this design! It was a fun project!

If I fold this again, I'll definitely use heavier paper: the standard origami paper that I used isn't stiff enough to form well-locked corners. (You can see in the photo that it's actually coming apart.)

Thank you for putting this up here. I've always wanted to fold this but I could not for the life of me find the diagrams. I've also made Gasherbrum, and Makalu, and currently working on double Makalu. If you want to see the pictures they are on my flickr page:

https://www.flickr.com/photos/93418464@N07/

Looks fantastic, well done!

The diagrams are in the origamiUSA magazine issue of 2002 (I think).. But ya I agree, they were freakishly difficult to get hold of!

Byriah Loper has done some nice adaptions of the 20 intersecting triangles theme.

Happy folding!

Note: This is not my original work, this was originally designed by Robert Lang.

However, diagrams are impossible to find on the internet, and I would like other people to have the opportunity to make this beautiful model as well. So enjoy :)

Robert Lang's work is always impressive.

http://www.langorigami.com/art/gallery/gallery.php?name=k2

I detect a hint of spitefullness? :) I never claimed to have designed the model, all I did was make the instructions available to the public... If you want the diagrams, they are in the Origami USA annual collection of 2002 (But you'll have to pay for them!)

No, indeed -- to praise the one is not to damn the other. These are some very nice instructions.

But if you're asking me, I do think it important to give credit to the creator of a model and to ask permission, when appropriate.

You are 100% right actually... i'm probably gonna get into trouble one of these days...

I offer a humbled bow in you're general direction!

Awesome instructable- admirable zen-patience.

Many thanks :) I wonder what the attempts-vs-"views" ratio is for this instructable...

As soon as I saw it I knew it was your work and looked for the Escher one. yes there it is. Love it and admire your patience. Great Inst.

Thanks :)

I appreciate the positive feedback! It's nice to know that my work is enjoyed :)

I don't get step number 4?

You need to fold the whole bottom edge up. There needs to be a line between the 2 short edges, connecting the guideline folds you just made.

The photo on step 5 shows it nicely :)

This is quite a difficult fold, try to do it accurately. I found the best was to fold it bit by bit along the bottom, keeping the distance from the top edge kind of equal all the way. See what works for you.

Looks amazing!

That is impressive!!

Looks hard! :b