Before revision:  We show that isolating cycles in polyhedral graphs can be extended to larger ones: every isolating cycle C of length 8 \leq |E(C)| < \left \lfloor 2{3}(|V(G)|+ 3)\right \rfloor implies an isolating cycle C' of larger length that contains V(C).
After revision:  We show that isolating cycles in polyhedral graphs can be extended to larger ones: every isolating cycle C of length 6 \leq |E(C)| < \left \lfloor 2{3}(|V(G)|+ 3)\right \rfloor implies an isolating cycle C' of larger length that contains V(C).