Floor panels like these can be seen in the Vulcan Learning Pods where young Spock (Jacob Kogan) is in school. Six of them make up the round base of the Pod.
They are thick Plexiglass (about half an inch thick) and very heavy. The designs are silkscreened on to the plastic and a white film of some kind is pasted on behind that. They were lighted from below.
A great resource for more on Scott Chambliss' designs from Star Trek (2009) is the book: "Star Trek: The Art of the Film" by Mark Cotta Vaz.