Relative lattices from finite point sets are finite in number, but convex lattices are uncountable for n ≥ 6.
The density of iterated crossing points and a gap result for triangulations of finite point sets, in: Proceedings of the 22nd Annual Symposium on Computational Geometry, pp
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Finite versus uncountable convex lattices from point configurations
Relative lattices from finite point sets are finite in number, but convex lattices are uncountable for n ≥ 6.