This is only a remark about one polygonal region $S$, a square.
As mentioned in this posting, I computed numerically the max volume shape that can be made from any folding of a square. Here it is:
The red path is the boundary of the square, perimeter-halved and joined as shown. Figure from Geometric Folding Algorithms: Linkages, Origami, Polyhedra.
I have no insight into what makes this the max volume shape, and I suspect this is a difficult problem for arbitrary $S$.
This is only a remark about one polygonal region $S$, a square.
As mentioned in this posting, I computed numerically the max volume shape that can be made from any folding of a square. Here it is:
The red path is the boundary of the square, perimeter-halved and joined as shown.
I have no insight into what makes this the max volume shape, and I suspect this is a difficult problem for arbitrary $S$.
This is only a remark about one polygonal region $S$, a square.
As mentioned in this posting, I computed numerically the max volume shape that can be made from any folding of a square. Here it is:
The red path is the boundary of the square, perimeter-halved and joined as shown. Figure from Geometric Folding Algorithms: Linkages, Origami, Polyhedra.
I have no insight into what makes this the max volume shape, and I suspect this is a difficult problem for arbitrary $S$.
This is only a remark about one polygonal region $S$, a square.
As mentioned in this posting, I computed numerically the max volume shape that can be made from any folding of a square. Here it is:
The red path is the boundary of the square, perimeter-halved and joined as shown.
I have no insight into what makes this the max volume shape, and I suspect this is a difficult problem for arbitrary $S$.
