More than Three Puzzles

This is a remix of "Three Related Tiling Puzzles" by pmoews.
I went down the rabbit hole of files, explanations, sources and links that he provides. You should too!
He has created an amazing assortment of puzzles, 2D, 3D, all sorts.

For a remake of this puzzle where you start with six pieces.
numbers: 12, 20, 23, 24, 31, 32
And interchange a seventh creating new puzzles.
I noticed that of the 108 heptominos"
There are 58 that can be swapped in:
12 that can go in with one part centered in the puzzle 34 39 42 59 61 68 74 76 85 88 91 96
8 more which only fit one way. 36 37 53 71 72 94 95 102
31 more that also fit to complete the puzzle.
So I uploaded the files with these groups in mind. Just don't check my math.

And there's also a box.