Here are the scale models of each heptomino six times as wide
and three times as high. In this case 6x6x3=108=all pieces are used. In the applet you can choose the number of the
heptomino (1..108) and the number of the layer (1..3).
Putting the heptomino with the hole in one layer, a heptomino from another layer
must fill the gap and a second one must balance the number of cubes in each layer. This was done by hand and
the rest of the layer was filled by computer.
Modelling each heptomino (scale 1:2 with 8 pieces, scale 1:3 with 27 pieces or
scale 1:4 with 64 pieces) doesn't seem as difficult, because only
few heptominoes are needed.
On the other hand many pieces are to large to fit the model due to the small edges. Are all these
problems solvable? I haven't tried yet. What are the highest n for models two times or three times
as wide and n times as high?