The aircraft, one of only a few flying machines still operating after the apocalypse, is a highly-modified military VX-4. It is capable of vertical takeoff and landing (V) with an X-wing configuration (X) and four engines (4). Originally built as a weapons platform that could also haul troops and cargo, I think of it as a cross between a V-22 and an A-10.
Horn has scrapped its original nitrogen-burning engines and replaced them with old petroleum-fueled jets. Fortunately the airplane carries a Portable Field Refinery Unit (PFRU) onboard, which comes in handy in the Slicks where there’s virtually an endless supply of crude.