What name is given to the center of a hurricane or cyclone?

The eye is a region of mostly calm weather at the center of tropical cyclones. The eye of a storm is a roughly circular area, typically 19–40 miles in diameter. It is surrounded by the eyewall, a ring of towering thunderstorms where the most severe weather and highest winds occur. The cyclone's lowest barometric pressure occurs in the eye and can be as much as 15 percent lower than the pressure outside the storm.

Source: Wikipedia