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There are lots of polymers, many of which do not contain ring structures. You will need to be more specific as to which polymer you're talking about.

One common polymer that does contain rings is polystyrene, in which the rings are simple phenyl rings hanging from a long-chain hydrocarbon backbone. There are also polymers in which the rings are in the backbone, such as poly(ethylene terephthalate) and Kevlar; again, these are phenyl rings in both cases. However, it's certainly possible for there to be rings other than phenyl groups in a polymer.


(A phenyl group hanging from the backbone has a formula of C6H5; one that's in the backbone will likely be C6H4, since it needs to connect at two points.)

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