Can periscopes have more than two bends? Is it theoretically possible to make a custom periscope with multiple bends at different angles? 
For example, a periscope that went from the bedroom, down the hallway, down the stairs, around the corner, and out the front door? 
I assume that if one were to get all of the mirror angles just right and the scope material was perfectly sealed it would work just like a regular periscope.
 A: 
The use of Porro prisms inside binoculars can be regarded as the two backward periscopes oriented perpendicularly.



The first prism forms a mirror image along one direction, the second one flips along another perpendicular direction. As a result, the device reverts the inverted image formed by two convex lens in the telescope.  Besides reverting the orientation of image, it can shorten the length of binoculars. However, the prisms make the binoculars heavy.



Also, pentaprism is used to bend the way of sight in a perpendicular manner.



A: I think you've already answered your own question. This is, of course, possible, but it's fairly difficult to align things precisely. You can, for example, put two normal (two-mirrored) periscopes together, so you have a four mirror periscope. If you want to look around many corners (so not only around the corner at the end of a street, but through a lot of streets throughout the city) you have to use very long pipes, connecting the periscopes at every corner. But if the mirrors are perfect I can see no reason why (in principle) this can't be done. 
