Step 1: Read the question.
We must say in which region the Antarctic ice shield lies.
Step 2: Earth's main regions.
By heat and latitude, Earth has the hot equatorial and tropical regions near the middle, mild temperate regions, and very cold polar regions near the poles.
Step 3: Where Antarctica is.
Antarctica is the continent that surrounds the South Pole. It lies almost fully inside the Antarctic Circle.
Step 4: Its climate.
Because it sits at the South Pole, Antarctica is one of the coldest places on Earth and is covered by a huge sheet of ice all year.
Step 5: Pick the region.
A place at the South Pole, covered in permanent ice, clearly belongs to the polar region.
Step 6: Conclude.
The Antarctic ice shield is in the polar region.
\[ \boxed{\text{Polar region}} \]