The edge pieces aren't symmetrical (!), with differently shaped holes on either side at different radii. You could put small magnets in there along with magnets in the corners, but consider these. (i) There's only one layer of plastic between the magnets (so ~1 mm) rather than two. (ii) For the hole further away from the core, the magnets in the edge have to be really tiny, like 2×1 tiny. (iii) For the hole nearer to the core, there's a bit more space, and maybe a 3×2 or 4×2 might fit. (iv) If you magnetise only one of the two holes, there may be polarity-related issues. (v) Regardless, the faces won't have a consistent magnetic pull, although the inconsistency might or might not be noticeable.
You could also place the magnet "on the side", so (e.g.) the north pole faces outwards (as in outside of the puzzle) and the south pole faces inwards (as in towards the core), which would eliminate polarity concerns and allow for larger magnets, but side-to-side magnetic attraction is much weaker than face-to-face attraction.
The corner pieces have a "unified" design (not split pieces, not exterior caps), although on each corner, one of the interior faces is a removable cap, so you can still place magnets on the inside. It could be possible to magnetise just the corners and forget about the edges entirely (like a 2×2×2), but there is an inherently large distance between the two corners due to puzzle geometry (~7 mm at minimum), and the magnetic strength calculator is telling me there's essentially zero force between the magnets if we constrain the magnets to be small enough to fit within the pieces. (Increasing magnet diameter also forces them to be further apart; with 5 mm diameter magnets, the distance has to be at least ~11 mm, I think.)
