  Consider a curve $\Gamma$ in a domain $D$ in the plane $\boldsymbol R^2$.
Thinking of $D$ as a piece of paper, one can make a curved folding $P$ in the
Euclidean space $\boldsymbol R^3$. The singular set $C$ of $P$ as a space curve
is called the crease of $P$ and the initially given plane curve $\Gamma$ is
called the crease pattern of $P$. In this paper, we show that in general there
are four distinct non-congruent curved foldings with a given pair consisting of
a crease and crease pattern. Two of these possibilities were already known, but
it seems that the other two possibilities (i.e. four possibilities in total)
are presented here for the first time.
