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Q: How many lattices does it take to cover a regular $n$-gon?

RavenclawPrefectGiven some positive integer $n\ge 3$, we can ask how many 2-dimensional lattices $L_1,\ldots,L_k$ are required such that their disjoint union contains all vertices of a regular $n$-gon. (We don't require that the lattices be centered at the origin.) When $n=3,4,6$, the polygon is a lattice polygo...

Grabbing that one. May be difficult, but we'll see if someone can say something useful.
@JyrkiLahtonen Would maybe be a suitable tag? What about ?
Since the question was bumped by the bounty, perhaps it is a good opportunity to improve tagging.
I'd guess could be added, if nothing else.
Thanks for the suggestion @MartinSleziak. I added a few tags, feel free to add whatever you think fits. I don't think is a very useful tag here.

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