After 3-4 attempts of making a ring of hexagons the light finally came on and I realized I was approaching the challenge from the wrong angle. (The model helped clarify this thought) At that point I started building / calculating from the top down and that made it all work. This took two approaches
- If you analyse the sphere closely again you will notice that if you level off the pentagon on top, you can create a series of slices through the points. This in turn makes a series of planes in space.
- If you can project that silly pentagon vertically through the whole thing you can use the points to control the needed points on a circle on those planes. Trig is still needed to find the radius of the circle but with perpendicular lines you can create the point in space based on an intersection of the perp. line and the circle.
I haven't failed. I've just found 10,000 ways that don't work.
-Benjamin Franklin
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