Consider a polygonal sheet $P$ of area $A$ with $N$ vertices (it material is not stretchable or tearable). Let $n$ be a positive integer >=2.
Question: Let $P$ lie on a flat plane. We need to fold up $P$ so that it now occupies only an area $A/n$ of the plane. It is also needed that the folding is as uniform as possible - ie the number of layers of the material above any given point should be as close to $n$ as possible. We need an algorithm that does it and an estimate of its complexity.
Example: If $P$ is a rectangle of area $A$ and $n$ is an integer, it is easy to see that we can fold it to an area $A/n$ such that it is exactly $n$ layers thick throughout - the 'creases' could simply be $n-1$ equally spaced parallel lines. It appears that no other shape of $P$ has this property of 'perfectly uniform foldability'. Which is the shape(s) of $P$ that causes greatest variation in the number of layers for a given $n$?
Further possibilities: One can further ask: Minimize the perimeter of the area $A/n$ region that is covered by the folded polygon. Alternatively, We could require $P$ to be folded as uniformly as possible so that it can be packed into a rectangular or square box of some specified dimensions - and area not necessarily equal to $A/n$ with n an integer.