This video explains how to make an Origami Icosahedron (designed by Heinz Strobl) using 50 strips of paper. You need 20 strips of a single color for the triangles and 30 of a contrasting color to connect the triangles.
Ancella Simoes is the author of the Origamiancy Blog and creator of all the Origamiancy origami tutorial videos on WonderHowTo. From Ancella's site:
"I fell under the spell of Origami early 2008 and have come to love folding new models and designs, so much so that it is now one of my favorite pastimes! Generally, I look up diagrams on the Internet, but I also own a few, very good, Origami books, which come in real handy."
This video demonstrates Ancella's technique for folding an origami icosahedron.