Usually polycube constructions are beyond my capability, since I don't own any physical sets beyond the tetracubes and have a computer that would probably struggle to find things with sets much larger than pentacubes. (I think hexacubes have a checkerboard parity issue just like the hexominoes as well, which makes the prospect all the more terrifying.) But recently I realised something about the set of thee 108 planar heptacubes that could make a few solutions possible despite only owning a set of bog-standard heptominoes.
Of the planar heptacubes the only one that really needs any special attention is the harbour heptomino equivalent. Unlike the case with regular heptominoes it doesn't force a hole in the construction, but it does sort of require that it must be placed perpendicular to whichever heptacube is filling its hole. At some point a few days ago I realised that if the harbour heptacube (it feels weird calling it that somehow) was 'neutralised' by a small number of pieces then I could solve the rest of the heptacube construction purely in layers using my existing set of heptominoes. Saving me from having to cut up and glue 108 pieces. Which I'll do eventually, just not now. The tetracubes were already pushing the limits of what I can make.
It turns out that two other heptacubes are enough to make a little bullet-heptomino-prism that can be slipped into the corner of a 3x14x18 cuboid, leaving three layers with a multiple of 7 cubes that can be solved manually. Something similar is probably possible for a 6-layer cuboid, 6x9x14 maybe.
Or a 4x9x21... And solving into four rectangles is a lot less painful than solving six... Anyway, here it is:
As usual, dots indicate that a piece extends down into the layer below, and a little square means it extends up into the later above. In this case the three heptacubes that lie perpendicular to the plane so to speak are the analogues of the pi and harbour heptomino and the one that looks like a little H inside a 3x3 box.
Here's a view of it as a nice isometric image, a needless victory lap purely because I learnt how to use Inkscape recently and want to show off:
If I can ever manage to solve anything with the larger polyiamond sets, at least it'll guarantee that the images on that blog post will look better than the old ones do.
EDIT sort of: A few hours after writing this, the urge to solve the 4x9x21 became too difficult to resist, and after about an hour or so I had the following solution using the exact same trick as the 3x14x18 for dealing with the harbour piece:
If I ever do make a set of these pieces, a box that holds them in a formation like this would be really nice probably. EDIT: Just after I first posted this post I got a comment pointing out something I should really have spotted sooner - the 'H' heptomino in these constructions goes through the central hole of the harbour heptomino, so unless the pieces were made of something really flexible (like rubber or very soft foam or something) there's no way you'd actually be able to assemble any of these physically.
