icosahedron

An icosahedron consists of 20 equilateral triangles.  (google it, and follow the links for "platonic solids")  The shapes below are made from 15 squares, five forming the top dome, five on the bottom bowl, and the last forming a belt into which the top and bottom are both inserted.  From Tomoko Fuse's book on unit origami.   (Yes, there are ten equilateral triangles in the "belt" for a total of twenty triangels.)   Overall strategy is to fold the square with 60 degree (120 degree) angles to form the triangles,