Rotating Zigzags Into Stars

The other day I came across a design that looked like it used only lines zig-zagging at right angles and I thought, "I could do that."

I made a mistake working from memory and forgot that I was supposed to be using a zig-zag and used squares instead.  But eventually I got the source pattern in front of me and saw my misstep.

Why yes, you could cut this design out on paper and then fold it into a truncated icosahedron; why do you ask?