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Fault-tolerance of a system measures its working capability in the presence of faulty components in the system. The fault-tolerant partition dimension of a network computes the least number of subcomponents of network required to distinctively identify each node in the presence of faults, having promising applications in telecommunication, robot navigation and geographical routing protocols. In this paper, certain triangular mesh networks including, triangular ladder (<inline-formula> <tex-math notation="LaTeX">$Tl_{s}$ </tex-math></inline-formula>), triangular mesh (<inline-formula> <tex-math notation="LaTeX">$T_{s}$ </tex-math></inline-formula>), reflection triangular mesh (<inline-formula> <tex-math notation="LaTeX">$rl(T_{s})$ </tex-math></inline-formula>), tower triangular mesh (<inline-formula> <tex-math notation="LaTeX">$Tr_{s}$ </tex-math></inline-formula>) and reflection tower triangular mesh (<inline-formula> <tex-math notation="LaTeX">$rl(Tr_{s})$ </tex-math></inline-formula>) networks are discussed for their partition and fault-tolerant partition resolvability. In this regard, it is shown that the partition dimension of these networks is 3, whereas their fault-tolerant partition dimension is 4.