Paper: 12 rectangles with a ratio of 1 by sqrt(2); here: 7.4 cm by 10.5 cm (3 in by 4 1/4 in), kami
Model in the collapsed state: diameter of 7.5 cm (3 in)
This video describes how to fold an action origami toy called Vertigo designed by Francesco Mancini. It's really fun to play with!
I recommend you use heavier, stiff paper. Elephant Hide works excellently. You can also try using a light card stock.
Francesco kindly gave me permission to make this video accessible to you.