The air gap in a transformer seems to always be spaced across the cross section of the core, where the magnetic field in the core has to then flow across it.
Since the core is typically made of stacked laminated sheets, it seems like it would be easier to construct an air gap by putting a sheet of plastic, or some other non ferrous material, in between the laminated sheets when stacking them. As far as I know, this is never done - why not? The stacking factor accounts for tiny gaps between sheets where the lamination material is - what would happen if one of those gaps were made larger?