The DC-X, short for Delta Clipper or Delta Clipper Experimental, was an unmanned prototype of a reusable single stage to orbit launch vehicle built by McDonnell Douglas in conjunction with the United States Department of Defense's Strategic Defense Initiative Organization (SDIO) from 1991 to 1993. After that period it was given to NASA, which upgraded the design for improved performance to create the DC-XA.
The DC-X was never designed to achieve orbital altitudes or velocity, but instead to demonstrate the concept of vertical take off and landing. The vertical take off and landing concept was popular in science fiction films from the 1950s (Rocketship X-M, Destination Moon, and others), but not seen in real world designs. It would take off vertically like standard rockets, but also land vertically with the nose up. This design used attitude control thrusters and retro rockets to control the descent, allowing the craft to begin reentry nose-first, but then roll around and touch down on landing struts at its base. The craft could be refueled where it landed, and take off again from exactly the same position — a trait that allowed unprecedented turnaround times.
In theory a base-first re-entry profile would be easier to arrange. The base of the craft would already need some level of heat protection to survive the engine exhaust, so adding more protection would be easy enough. More importantly, the base of the craft is much larger than the nose area, leading to lower peak temperatures as the heat load is spread out over a larger area. Finally, this profile would not require the spacecraft to "flip around" for landing.