That is very pretty obsidian you have pictured. My concern with faceting would be the air bubbles. If you think you can get a clean piece it may be worth trying. I’ve never faceted synthetics or glass, but faceted obsidian pieces are beautiful. Take a look at some images on the web. That said, care should be taken. I once dropped an obsidian cab piece on my kitchen tile floor. It broke into several pieces as expected, but like all glass is also broke into some tiny and very sharp splinters. Maybe try a smaller piece to see how it feels on the machine. You may have found your perfect medium. Good luck!