Attempt 1 at the monkey saddle.
Attempt 5 at creating a regular hexagon from a regular 8.5 by 11 sheet of paper.

This origami is a representation of the function z = x^3 - 3xy^2 which has been noted as having a “monkey saddle.” I believe it refers to the 3 depressions where a monkey could put his 2 legs and tail in.
The function has only an inflection point in the center as opposed to a local min or max (depending on plane of intersection) as seen in a hyperbolic paraboloid or similar function.