Find the surface center of each face (geometry nodes)

It is relatively straight-forward to compute the center of mass for each face:

(By triangulating and computing the weighted average of the triangle positions, their relative face area being the weighting factors).

center_of_mass.blend (113.0 KB)

If you are interested in the bounding box, you first have to define a coordinate system in which to compute the box. You can look at this thread here to compute statistics per face in order to get a bounding box for every face:

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