I planned to make a guide on how to make a paper icosahedron, but I never got to that. This isn't exactly a guide, just a picture of the measurements you essentially need to create one. Below is a diagram that shows a map of a "cell" of an icosahedron. By "cell," I mean if you were to split a filled icosahedron into 20 symmetrical pyramids (it turns out, the pyramids are REALLY close to tetrahedrons), the "cell" is what you'd get. The measurements are basically ratios, treating the side length of the equilateral (center) triangle as 1.
I usually take 20 index cards (6x4, but any size works), multiply the coordinates by whatever scale factor makes the 1.675042398 number 4 (or 3, if you're using a 3x5, or any other paper honestly), and drawing the diagrams onto the papers. I then cut them out, fold them, and tape them together (or glue, I've never tried glue yet) such that the equilateral faces are facing out. Then, you end up with an icosahedron!