Heard of a three-inch turntable? The model, "Triple Inchophone", was made by Japanese company 8-Ball Bandai. Dedicated vinyl geek Jack White decided to reissue some of his old White Stripes material in a unique way; thus he commissioned them to make a limited number (400 or 1000 from research) special edition 3″ record players, and a very limited number of 3″ singles to go with them. They’re pretty rare these days, but do come up on eBay sometimes.
Meanwhile, DJ Nu-Mark seems to have got some 3″ time-coded records cut and handles them better than most handle 12″s. Watch him go in the video from the 15 minute mark below: