Solutions for Act II Scene 4 - Duplex

The title suggests that the two images should be printed back to back on the same piece of paper. You'll notice that the shapes match up and the dashed lines manage avoid each other completely. The next step is to fold the piece of paper using valley folds wherever the dashed lines can be seen.

Now cut out the shape along the solid lines, then try to fold it into a solid according to the folds made in the previous step. This can get a little tricky as you will need to slide two loose ends through the gap in the middle. This should be doable in a way so that all grey squares are covered up exactly. The following staircase-like shape is obtained. Note that the two images has the opposite orientations, you may need to squint to see the one on the right correctly.

All the paths that led to nowhere now connect up properly. The shining blue ball suggests a starting point for the next step: to find the path connected to the blue ball. On the surface, the path ends quite quickly. But if we consider each end point of the path to be connected the same point on the other side of the paper (an idea consistent with the theme of the puzzle so far), it's possible to proceed much further. Continuing along, and wrapping around edges of shape when indicated, the path eventually returns to the starting point, forming a loop.

It is possible to view the shape in six different perspectives such that exactly four squares are visible each time. If we focus only on the circles belonging to the path found above, we obtain the following letters.

The answer is galaxy.

The answer is: galaxy