Fold a Hyperbolic Paraboloid

A square piece of paper with accordion-folds running parallel to each edge of the paper naturally takes on the form of a hyperbolic paraboloid. Eric Demaine invented this model.

Steps

1. Print out the pattern and score the fold lines. (Or follow the directions on Erik's website. See link below.)
   
2. Fold accordion style by alternating mountain and valley folds.
   
3. Pinch the folds together from the middle of the outside edge to the middle of the square to help you make strong creases and crease the corners.
   
4. Partially open the shape so see the hyperbolic paraboloid.
   

Links

• Erik Demaine shows how to fold this hyperbolic paraboloid without a pattern. He also assembled them into models of solids based on the Platonic solids that he calls hyperhedra.

References

• (Peterson 2001, 79-80)