If you've ever had an idle moment to wonder whether Homalomena cuttings could be propagated by rooting them in water but then didn't actually try doing it because you're a busy person and you have more important stuff to do (and most things are more important than rooting Homalomena cuttings: you made the right choice), the answer is a qualified yes:
The back story here is that my Homalomena 'Perma Press' had gotten very tall and floppy, plus it's never been a particularly full-looking plant because it's been stuck inside in less-than-ideal conditions for most of its life. So I finally got fed up with it and cut the tops off the two long stems. I didn't want to just throw them out, especially since I didn't know if the stumps would resprout, so I put them in water, and voila.
The stumps are capable of resprouting, as it happens, though that doesn't necessarily mean that they'll always do so:
The ultimate plan is to stick these rooted tops back in the pot with the original plant, in hopes of getting a more presentable specimen. The transition from water to soil is hard for a lot of plants, but aroids (with the exception of Epipremnum aureum) usually handle it well, so I'm optimistic. I should probably do this sooner rather than later, because the roots are getting longer, and I'm not maintaining a high water level in the vase very well.