Make each side have no duplicates. Every letter has to be different on each side.
I also added chamfer sides as an option.

I went to the effort of figuring out how to figure out a combination of letters that only has 1 solution. I deliberately scrambled the solution as on my printer you can often see that the side printed flat on the print bed is slightly different than the other sides.
I did solve it, so there is at least one solution.

By my calculations there are 4^5 different combinations which makes 1024, and only 1 that works.
I guess the other challenge is how many different words can you spell?
I know one person solved this in less than 15 minutes, and another did it in approximately 3 minutes, so it is not a really difficult puzzle.