So if you repeat that with all 12 edges you'll get surfaces like the attached.

It still needs some problematic bunching and slivery intersections to resolve but it's 12 surfaces to work with instead of a whole lot of arrayed solids so probably better.

If some extra space is ok maybe something like arraying a cutting plane along the path and intersecting those with the 12 surfaces could yield some cross sections.

- MIchael