I don't know what an infinite family, isolate, or sporadic is. A quick Google search didn't make it obvious.

I think 8 pieces also works, but I think that may be it.

An infinite family seems to refer to an infinite collection of solutions that are all related in some sense. An isolate or sporadic solution is a solution that is unique and unrelated to other solutions. They are both terms used to categorize solutions.

Thanks nocipher for the definitions. From this I see no sporadics. And two infinite families, at least how I'd classify a family.

nocipher's definition are correct.

And I have, so far, 5 infinite families with, respectively, 2, 4, 8, 16 and 32 pieces.

But details matter, and you might start to question what it really means when I say "piece." Does the definition I've given really capture your intuition?

But I need to go back to writing the article.