M. JONSSON, J. WÄSTLUND, PARTITIONS OF R 3 INTO CURVES, Mathematica Scandinavica, Vol. 83, No. 2 (1998), pp. 192-204

We prove that, for any two polyhedral manifolds P, Q, there is a polyhedral manifold I such that P, I share a common unfolding and I, Q share a common unfolding. In other words, we can unfold P, refol...

We resolve the moving sofa problem by showing that Gerver's construction with 18 curve sections attains the maximum area $2.2195\cdots$.