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Is there a special term or convenient phrase for the restriction of a convex region to points of a lattice?

This is motivated by wanting to talk about the feasible points of a discrete problem. I'd like to say the points form a convex region, but since they are a subset of the usual integer lattice in several dimensions, that's not AFAIK correct terminology.

I note that convex lattice polytope refers to the (connected) convex region and not to lattice points contained therein.

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    @QiaochuYuan: I invite you to post your comment as an ans$w$er. Although a "negative" ans$w$er, it will be gladly accepted.2012-08-26

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