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A family \(\mathcal{G}\) of connected graphs is a family with constant metric dimension if \(\dim(G)\) is finite and does not depend upon the choice of \(G\) in \(\mathcal{G}\).
The metric dimension of some classes of plane graphs has been determined in \([3]\), \([4]\), \([5]\), \([10]\), \([13]\), and \([18]\), while the metric dimension of some classes of convex polytopes has been determined in \([8]\), and a question was raised as an open problem: Is it the case that the graph of every convex polytope has constant metric dimension? In this paper, we study the metric dimension of two classes of convex polytopes. It is shown that these classes of convex polytopes have constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of these classes of convex polytopes. It is natural to ask for the characterization of classes of convex polytopes with constant metric dimension.