Horseshoe Flattop - an extremely short version of the flattop cut. This cut gets its name because the only hair left on the head is a "horseshoe" shape ring of hair around the upper sides and across the front. The "landing strip" area is bigger than in regular flattops and the unguarded clippers are taken over the crown of the head. One contributor to this website provided some more information about this cut, also calling it a "TH flattop". This is described as a flattop cut with a TH clipper. The TH clipper is a type of clipper that will cut hair even closer than the 000 Wahl or 0 Oster clipper and is almost as short as an electric shaver.
The horseshoe flattop is also sometimes known as a "burr with bumper". The cut is basically 1/4" (no more than 3/8") butch waxed in front and an 1/8" along the sides of the "flat" - it's as short as you'll get before going to the full burr or induction cut. It was popular among career Marines in the 1960's. Unlike most other flattops, this cut can work well with fine or thinning hair (or at least some types hair thinning patterns). (Thanks to Gunny for contributing this information.)