This morning, my sister and I were discussing whether to make use of a litterbox for Buchi or any small-breed dog she may have her eyes on. I told her yes but forgot to mention that cats and dogs usually have different litters composition.
Cats prefer to cover their poops with sand (because it's easier) while dogs do so more seldom than often. And if ever they do the scuffing/ kicking/ wiping their feet action, given that you have a cat litter, such action will remove a fair amount of kitty litter from the box.
So as for the question, should they share one litterbox? The answer is no. If the cats were to see the sand submarines in their boxes, the tendency is that they would find somewhere else to do their deed. Peculiarly enough, dogs might find it an interesting outdoor snack seeing cat poop on where they're supposed to defecate and eat rather than eliminate there. So the answer is still no.
And by the way, I've read that cat litters are bad for the dogs tummy. To make it more worst, the litter hardens in their tummies once ingested.
One more thing, the term Coprophagia is used to define dogs eating cat poop.