Nothing says disgusting like having an open box full of your cats urine and fecal matter sitting out in your bathroom or kitchen. Sure, a cat's gotta do what a cat's gotta do, but try to retain some dignity in your home. I mean, really. You're the master, not the cat, right?
Just get something like this unfortunately-named "Kitty Washroom." It's a little bathroom for your cat that goes in your bathroom, giving the little feline a bit of privacy, and, even better, a place to hide its dirty business out of your sight until you decide it's time to clean up after it. Hey, it's easier than toilet training the cat, isn't it?