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Suppose we have a convex hull computed as the solution to a linear programming problem (via whatever method you want). Given this convex hull (and the inequalities that formed the convex hull) is there a fast way to compute the integer points on the surface of the convex hull? Or is the problem NP?

There exist ways to bound the number of integer points and to find the number of integer points inside convex hull, but I specifically want the points on the hull itself.

EDIT: Suppose the set of inequalities (the linear program) have integer coefficients /EDIT
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Finding Integer Points integer points on an N-d convex hull
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Finding Integer Points on an N-d convex hull

Suppose we have a convex hull computed as the solution to a linear programming problem (via whatever method you want). Given this convex hull (and the inequalities that formed the convex hull) is there a fast way to compute the integer points on the surface of the convex hull? Or is the problem NP?

There exist ways to bound the number of integer points and to find the number of integer points inside convex hull, but I specifically want the points on the hull itself.