This icosahedron is based on three intersecting golden rectangles. The project is easy to construct from plywood, but there are also plenty of crafting alternatives that do not require power tools. The icosahedron is one of the five Platonic solids. It has 20 faces, all of which are equilateral triangles.
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Template:
http://s5.postimg.org/qw8239447/golde...
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About my mathematical scribbles near the end:
Yes, I know that I used 'r' as a variable twice, but I ended up not using the 1/6 arc. In fact, the problem turned out to be really simple, and so I only used geometry, the Pythagorean theorem, and some ratios to answer my question.

See, math (as used in real life) is mostly just thinking out loud and stating the obvious, because that's what a systematic approach to an investigation does. It's like tire kicking, because you are uncertain about something, or else you wouldn't be doing a math problem in the first place; you are, after all, amidst a problem by definition. Usually you are looking at some scratch sheet, and not at a finished piece of work. Yes, there are mostly redundancies all over the paper, but that's because I didn't know how to solve the problem at first, so I jumped right in by trying whatever popped into my head and step one is to define the things I do know.

I often think of mathematics as like having another sense like another way to see things. This sense can help us to gain a better conceptual understanding of the thing we are considering. Just as we have two eyes to give us depth perception, adding mathematical reasoning to the way that you look at the world will enhance the resolution of what you see, I promise.

Thanks for reading
pocket83