Again, this text is needlessly obscure. Dessins d'enfants (not "D'essins") relate to functions on the Riemann sphere corresponding to certain covering spaces—if there is any connection to "seeds" it ought to be explicated.

Given the context of the Rubik's-cube puzzle you mentioned earlier I have a very vague impression what you are attempting to do. Without which context, a reader would have no idea whatsoever.

Yes you’re right. In the future I’ll make sure my question can stand on its own.

I will provide preliminaries for those who would like to reference background material.

@zetaspace I mean, they might perhaps be interesting, even substantive questions—but I don't think anybody can tell. E.g. I likely have the most experience with the Fano plane and other such recreational-mathematics topics of any Codidacter; but even I couldn't make any sense of your previous question about the Fano plane.

In addition to providing preliminaries, I don't think this is even complete. How does $\mathcal S$ determine $p$, for example?

@Peter Taylor: See some other posts on this user's site, all of which are at least as unclear as this one, e.g. here.