The fault-tolerant resolvability is an extended version of vertex based resolvability in simple connected graphs with various intelligent system applications, for instance, sensor networking, network optimization, and robot navigation. The uniform rate of transformation of data to all intersection points makes the rotationally symmetric graphs of convex polytopes significant in intelligent networks. Let \(\Gamma =\Gamma (V, E)\) be a simple connected non-trivial graph with edge set \(E(\Gamma )\) and vertex set \(V(\Gamma )\) . A subset \(\mathbb {R}_{v}\subseteq V(\Gamma )\) is called a vertex resolving set in \(\Gamma\) if for each pair of distinct vertices \(p_1\) and \(p_2\) in \(\Gamma\) , we have \(d(p_1,u)\ne d(p_2,u)\) , for some vertex \(u\in \Gamma\) . A resolving set \(\mathbb {R}_{v}\) with the minimum resolving set is called a metric basis for \(\Gamma\) . The cardinality of the metric basis is referred to as the metric dimension of \(\Gamma\) , denoted by \(dim_{v}(\Gamma )\) . If \(\mathbb {R}_{v}\setminus \{u\}\) is also a resolving set for each u in \(\mathbb {R}_{v}\) , then \(\mathbb {R}_{v}\) is called a resolving fault-tolerant set. The fault-tolerant metric dimension of \(\Gamma\) is the smallest size of such a set \(\mathbb {R}_{v}\) . In this paper, we investigate two families of convex polytope graphs, \(W_{n}^{*}\) and \(Z_{n}^{*}\) , in terms of their metric dimension and fault-tolerant metric dimension. We show that these parameters are constant for the aforementioned families of convex polytopes.
