The geometric center of a primitive in Second Life is the intersection of all straight lines that can divide that primitive into equal parts. In reality, as the geometric center of a prim is unaffected by such factors as Path Cut, Twist, Taper, Shear and Slice, which appear to alter the prim's physical proportions, it is the intersection of all straight lines that can divide the primitive's bounding box into equal parts that defines the geometric center. In some cases, prim torture parameters can cause the prim to appear to extend beyond its own bounding box, but its geometric center will remain unaffected.
The geometric center of an avatar's bounding box is similarly derived, and places it in the groin area of the avatar. The precise location of the avatar's bounding box geometric center is variable due to the ability to independently edit the various avatar shape parameters.