Crease pattern
mountainvalleynot decided
Folded
Darker means more sheets of paper lie on top of each other there. The paper only reaches this shape if a legal order of the layers exists.
Verdict
Click the creases.
0of 0 ways found
0valid assignments exist
0assignments in all
Every interior vertex
A vertex is green when it passes all three local tests: Kawasaki on its angles, Maekawa on its mountains and valleys, and an exact check that its own sectors can be stacked. Green everywhere is not the same as foldable.
One vertex, any angles
Set the sectors around a single vertex and watch two completely different methods count the valid mountain-valley assignments: Hull's recursion on the angles, and brute-force enumeration of every way to stack the sectors.
What the two methods say
| Hull 2003, Theorem 5 (recursion on the angles) | — |
|---|---|
| Enumerating every stacking (pure geometry) | — |
| Hull's lower bound 2n | — |
| Hull's upper bound 2·C(2n, n−1) | — |
| Assignments that satisfy Maekawa alone | — |