This is actually for a wood shop project... but it certainly involves geometry! I am trying to build a real-world regular icosahedron. I know I need 20 equilateral triangles for the faces. But I do not know what the angles of the sides/thickness should be, to join those 20 triangles into a 3D shape. Nor do I know how to calculate it. I'll be perfectly honest - this is not some homework or test that I *have* to figure it out for myself and show proof of work, so if someone wants to just post the answer, I am fine with that. But if you want to make me work for it, giving me the formula as a starting point, (and probably working with me to verify I solved it correctly) is okay too.

Thanks in Advance!