I met Paul

I  had a genuinely surprising moment the other day when this guy sat next to me on the tube and said " So... I'm not the only one." and was folding a 20 pointed star.  

He left a completed one on the seat when we left and gave me a piece of the puzzle to look at myself.  I am still grappling with the equilateral triangle that it all involves.  I have since found a way to make a tetrahedron( 4 equilateral triangles forming a regular geometric 3d object)out of 3 pieces of paper and a geodesic shape currently a rock or lump but it may grow into a icosahedron (a 20 sided object or D20 if you play role playing games).

Apollo 11

So.... having figured out the legs and dome then I had to divide my sheet into 7 parts (see attached diagram) and then do 4 legs, one for each corner. And there was Apollo 11 or at least what I had wanted to achieve.

The development of Apollo

So it took far too much fidgeting but I came up with a plan.  It was funny working on just one leg of the lander as I could see what I was working towards but it was just strange for anyone else to see I'm sure.

The final solution was to replace the tucked away  method for hiding the excess paper in the original fold with a petal fold exterior to the dome shape.

Then I tucked away most of the petal fold to the interior of the dome.  

I then folded the petal sides to the middle to create a long thin leg for my craft.

To finish I pinched the leg out in the middle and added a landing foot.

The birth of Apollo 11

Two strange things have converged in recent months:  the anniversary of the moon landings and a new fold (to me).  

The photos I have here are the shapes I came across fidgeting one day.  The indented equilateral triangle is a very strange fold as it makes an easy shift from a flat surface through two 45' bevels to 3 perpendicular sides each at 45' to each other.  This quite simple set of folds is an appealing shape in itself. 

 When you combine 4 of these around a square you end up with an octagonal based dome.  I loved the simple architectural properties of this shape and almost instantly likened it to the top of the Apollo 11 Moon-lander.  It has unfortunately taken me 4 months to figure out how to make the rest of the craft....