Margen
A desert isn't defined by heat but by thirst: less than 250 millimetres of precipitation a year. By that yardstick, the champion has no dunes. Antarctica, at around fourteen million square kilometres, comfortably beats the Sahara (about nine million) and is, officially, the largest desert on Earth.
Its interior receives roughly 50 millimetres a year, almost always as snow. And in the McMurdo Dry Valleys things turn absurd: dense, fast katabatic winds evaporate any moisture, and it's estimated that no rain has fallen there for about two million years. The landscape is so Martian that NASA uses it to test instruments bound for Mars.
The final paradox is perfect: the driest place on the planet holds, frozen, around seventy percent of its fresh water. The world's largest desert is also its largest water reservoir. It's just that nobody can drink it.