  For a connected graph $\Gamma=(V,E)$, a subset $R$ of ordered vertices in $V$
is said to be a resolving set in $\Gamma$, if the vector of distances to the
vertices in $R$ is unique for each $u^{i}\in V(\Gamma)$. The metric dimension
of $\Gamma$ is the minimum cardinality of such a set $R$. If $R\setminus
\{u^{i}\}$ is still a resolving set $\forall$ $u^{i}\in R$, then $R$ is called
a fault-tolerant resolving set (FTRS) for $\Gamma$ and its least cardinality is
the fault-tolerant metric dimension (FTMD) of $\Gamma$. In this article, we
introduce the concept of an independent fault-tolerant resolving set (IFTRS)
and investigate it for several well-known graphs. We also show that the FTMD is
four for three closely related families of convex polytopes available in the
literature (viz., double antiprism $\mathbb{A}_{n}$, $S_{n}$, and $T_{n}$).
