I like the idea of embedding n - 1 squares in each face, it is quite intuitive...but not fully satisfying. It would be nice if exactly six n - 1 squares would fit into the surface...but no, there are two additional uncovered cubelets. Two is again unintuitive to me - 6, 8 or 12 and I would be happy. On the other hand unintuitve results make me redo the work to find the mistake and so unintuitve results are less likely wrong and that in the end is a good thing.

After spending some more time thinking about my initial reasoning it became a bit more intuitive. I thought there are O(n^2) cubelets on each face and the error with the edges is only O(n) so the error should become negligible and it does - the linear error becomes a constant error of less than 1. I just expected it would approach 0 and this is not true.

And now I will stop bothering - my intuition is not the best in this area and I will just have to calculate everything. I just realize that I can not even easily say if the approximation over- or underestimates...we use some cubelets twice, so we under...over...underestimate the area of a face...no, over?...under!...