Propagating Papyrus plants is rather entertaining as they grow upside down! The plant shown here is Cyperus alternifolius (umbrella papyrus) I believe. I also did this same propagation with a Cyperus papyrus but it did not grow quite as well, perhaps due to higher light requirements.
Propagating this plant is super easy:
Step one: Cut off a stem of the plant.
Step two: Place upside down in water.
All done! Keep the water level relatively consistent, and place in the sunniest place you can find, either a south window or outside is best. I used a western window and had some success though the plant did much better once it got outside.
**Update: It's now been about a year total since I originally rooted the papyrus, and it's still doing great! survived and thrived in a western window all winter.