I came across a VIking Triangle Knot design. This inspired me to make one of squares (boring, ho hum) and Pentagons. It took me a while to figure out the correct ratio of strip width to pentagon size to make the tightest knot possible.
Oddly enough the solution to the Pentagon Strip thickness was in front of me the whole time. All I needed was to use the projected width from a top view of a dodecahedron. This shape continues to surprise me. :o)