ABSTRACT
In this paper, we focus on more combinatorial issues. Given a singlevertex crease pattern v with specified crease angles but no mountain-valley (MV) assignment, we may count the number of possible valid (physically realizable) MV assignments. This total, denoted C(v), can be determined in linear time [1,2]. If we know only the number of creases, say 2n, but not the crease angles, we can still obtain sharp bounds on C(v):
2n ≤ C(v) ≤ 2 (
2n n− 1
) . (1)
We know that C(v) is always even, as the MV parity of the creases can always be flipped. But can C(v) achieve all even values between the bounds in Equation (1)? The answer turns out to be “no,” which immediately
makes us wonder whether we could predict or classify the various values of C(v).
