Not 3D, but plexi. Not sure what to call these, how about "back painted".
Take some plexi and paint it [any color you wish, I use black].
2-3 coats a must to ensure coverage. When dry, etch your design [mirrored, same as any plexi design].
When done, next step for me is to spray the etch with matte clear coat, this to a degree restores lost transparency created by the machining.
With that done and dry, spray the etch with the color of your choice [I usually use white, just tried this yellow and it pops even more].
After this I spray the reverse back to black, purely cosmetic.
You can edge light them [white example is edge lit], but no sense using multi color, just white will do. Paint absorbs most of the light so its just a nice accent for those times where it might be displayed in the dark.
This union logo should be a hot seller on some of my big jobs, guys go gaga for stuff like this. But this method lends itself well to just about anything 2D, lots of options for creativity. I have been thinking about airbrushing a red/white/blue stripe flag design, etching a nice eagle on it and painting it black, that would look pretty slick. [Sorry if pics are upside down/sideways, these phone shots seem to come out that way often]
Designs are 12x12", 3/8 thick and were done with a drag bit. Could just as easily be done on .25 or .5 plexi, I like the extra depth of 3/8 vs .25.