1958 Chevrolet Corvette XP-700
It is based on a regular '58 Corvette and was modified to be the own car of William L. "Bill" Mitchell. First, in 1958, it received a special rear end of duck-tail type, which was incorporated in the regular '61 Corvette, and the front end was redesigned to look almost like the one of the Oldsmobile F88 '54 show car.
In 1959, the car was modified again to became a real show car (that's the one on your picture): longer rear end, new front end with smaller air intake, new transparent roof with a periscope in the middle of the two bubbles. The design of this car is not purely American. It was inspired by the '55 Lancia Aurelia 2500 GT Rayon d'Azur, mechanically modified by Nardi and body by Vignale. This Italian show car has a double-bubble roof with a chrome plated grille (air intake) in the center of the roof. The XP700 has the same feature, except that the air intake has become a periscope (more futuristic !).