Pretty trippy, right? Given that Antarctica rests on every line of longitude, you might be tempted to think the continent observes every single time zone, but this is not the case. In fact, as the maps featured here illustrate, even regions that lie along the same meridian don't necessarily observe the same time zones, due in large part to the range of territorial claims on the continent. Some places — labeled in red — have no time zone, and just observe Coordinated Universal Time, by default.
So much for running in a circle around the South Pole and traveling back/forward in time*. More info, including hi-res versions of the maps below, here and here.