Golf club head with variable face thickness

A face for a golf club head is disclosed herein. The face has an interior surface comprising a central region having a first perimeter having an elliptical shape, an outer edge having a non-elliptical, driver-face profile shape, a first intermediate region located between the first perimeter and the outer edge, the first intermediate region having a second perimeter with a shape that is more similar to the shape of the first perimeter than the shape of the outer edge, and a second intermediate region located between the second perimeter and the outer edge, the second intermediate region having a third perimeter with a shape that is more like the shape of the outer edge than the shape of the first perimeter. The thicknesses of the perimeters of the face disclosed herein may vary around their respective circumferences.