I was reading along in a great book called Why Buildings Stand Up [Salvadori] and I came across a cool folded paper arch. When properly supported laterally by buttresses, it can support a couple orders of magnitude above its own weight. It also looks great and can be a hat! Here's how to fold it.
Step 1: Start With a Piece of Paper
Start with a plain 8.5x11.
Fold into eighths along the long direction.
Then fold 14 diagonals in the opposite direction, using the ends of the first folds as guides.
I made poor creases on the first try (they didn't align with the edges of the first set of creases), but then had much better success using a pencil and a straightedge.
Step 2: Taking Shape
As you complete the diagonal creases, the sheet will begin to curl.
Finish the barrel by encouraging the folds so that the paper curls into a half-circle.
Eventually, it will fold up accordion style into a flat, rotationally symmetric 2D shape.
Awesome thin shell concrete roof: