Why do planes fly over the Arctic but not the Antarctic?

Several commercial air routes exist over the Arctic, but none over the Antarctic - why is this the case?

Why don't commercial flights fly over Antarctica?

While technically possible, risks like weather and visibility, and other factors refrain commercial flights from flying over Antarctica.
Smithsonian Magazine

A Century Ago, an Explorer and His Pilot Claimed to Be the First People to Fly Over the North Pole. Here’s Why Experts Doubt That Achievement

While the success of Richard Byrd and Floyd Bennett’s polar flight has been disputed, the former went on to accomplish ...