Dork Scratchings

In my previous post  Building a tensegrity structure I implied that when the thread was pulled taut an icosahedron would form.  I didn't directly use the word "icosahedron" but I did claim that you needed to allow enough thread for a stick length to triangle edge ratio of $(1+\sqrt 5)/2$, which amounts to the same thing.

 My latest project   This turned out to be a bit more fiddly than I expected.  This is partly because I set myself the goal of building it using a single piece of string and it wasn't entirely obvious how to do that without missing or repeating some edges.  Here are my tips:   1. Cut 6 pieces of bamboo Obviously these should all be the same length.  Hollow them out before going any further. 2. Measure out the thread The thread will pass through each bamboo 4 times, plus there are 24 edges between bamboo ends.  The bamboo sticks are $(1+\sqrt 5)/2$$^{[\text{see footnote}]}$ times the length of the edges (i.e. the golden ratio!)  You will need a bit more than this to make it easier to tie the ends.  Place two marks on the thread with a pen to identify where the knot should fall.   3. Blue tack the bamboo pieces in place This means creating a ball of blue tack and attaching 3 parallel pairs of bamboo to it in such a way that each pair is at...