Introduction: Gasherbrum - 4 Intersecting Triangles - Modular Origami - No Glue

Hi guys and gals :)

Time for something slightly easier!
This is the easiest of the 5 himalayan peaks by Robert Lang.

This model took me just over 2 hours to fold, and it's loads of fun! Doable in one sitting ;)

The maths:
These are 4 equilateral triangles that effectively form 4 triangular planes that intersect at a single point.
if you plot the points of each triangle in space you get an cubeoctahedron, which is a polygon with 8 triangular faces and 4 square faces.

What you will need:
6 sheets of square paper

Ok lets get started!

Step 1: The Paper

First things first!
Put on some nice relaxing music.

Colour schemes: Either make each triangle a different colour, or use a uniform random or chaotic design.
I don't particularly like the colour scheme I used with this one, I'll do it again sometime with nicer colours.

Start with the coloured side down, fold the paper in half and then unfold.

Fold the edges to the middle and unfold that as well.

Step 2: Folding

fold in half again in the other direction (bottom to top), but don't crease all the way across, just pinch the edges. These are just guideline folds.

Unfold and fold the top and bottom edges to the pinches you just made (dividing the paper into quarters), and once again don't fold all the way across, just pinch the edges.

Step 3:

Difficult step.

Fold the bottom RIGHT HAND corner to the LEFT side of the page, 1/4 from the top. Pinch the edge (more guideline folds).
This will be close to, but not on the 1/4 mark at the bottom left hand side.

See the photo.

Now fold the BOTTOM LEFT corner to the RIGHT side of the page, 1/4 from the top, and pinch the edge.

Repeat this process for all 4 sides.

Step 4:

Cut the paper in half along the first fold you made.

Step 5:

Fold the top edge down exactly where the diagonal pinch you just made touches the side of the paper.
You will notice (since you cut the paper in half) that these pinches are only on 1 side of the paper.

Make sure it's straight.

Do the same from the bottom up.

Make sure you fold from the DIAGONAL pinch, and not the straight pinch which is right next to it.

Step 6:

Fold the bottom left corner to the diagonal crease on the bottom of the paper. 
Follow this line all the way up, folding the left edge inwards, so that the top left corner also meets the top diagonal crease.

Note that this is not along the midline, but about half a cm to the left of the midline (depending on the size of your paper).

If you struggle to get a straight fold, take a ruler and crease the paper with an empty ball point pen.

Step 7:

Fold the right side of the paper under the left side, along the midline.

Turn the paper over and valley fold the long edge to match the edge underneath it.

When opened up the 2 long edges should be the same distance from the midline (see photos).

Step 8:

Fold the top right hand corner down from the midline to the crease you made in step 5.
Unfold this and do the same on the left side.

Unfold this, rotate the paper around and do the same on the bottom.

Note that the 2 creases don't fit perfectly into each other.

Step 9:

Sink the top right hand flap.

Fold the flap back along the midline and unfold (just to crease). This creates a "bent" pocket to lock the pieces together.

Rotate the paper 180* and repeat.

Well done, now fold the other 11 pieces.

Step 10:

To fit the pieces together, fit the flap of one piece into the pocket of another, and pinch the piece with the flap (or fold the pocket, either way) to lock the pieces together.

Lay the piece with the flap flat against the piece with the pocket, and insert the other flap into the other pocket (suggestive much??). Pinch or flatten to seal the join. The pieces will make a 60* angle when flat if done correctly.

Fold 3 into a triangle.

Fold a second triangle into the first one, and note the specific arrangement

Step 11:

Add a third triangle.
Note the specific arrangement, and copy it exactly.

Each triangle has to have one leg going through the center of each other triangle.

Step 12:

Adding the fourth triangle.

I found it easiest to do this one piece at a time, as the pieces will hold their place anyway.

Notice the clockwise weave on the picture, and copy that.

Step 13: Done!

That wasn't so hard, was it :)

Great job.