An icosahedron is a 20-sided shape. Four of us got together to make some. We had a good start the first evening and decided we'd finish tangling them at home and come together again to fold them and glue them together. One person decided to cut out the shape first and work on the back of the template so as not to have the triangle division lines.
Two views of the final products! Unfortunately, the one at the back is a little fuzzy. We added heavy thread so the shaped could be hung.
You can see another tangled 3-D shape I made here.
Go ahead, try this at home:
You can find an 8.5"x14" template here. I had the photocopy shop increase it to 11"x17".
Ideally it should be printed on heavy paper or card stock. You want it to be sturdy but also to fold easily.
You'll need glue that will dry quickly and not buckle. Many liquid scrapbook glues with a fine tip nozzle are good this way ( have Elmer's and Scotch, both good). The last few tabs you glue will be tricky; be forewarned.