I don't think this would work. If every carbon was part of cumulated polyene, then the preferred geometry is linear for most of the carbons. Adding more carbons will not help. They all still want to be linear. Not to mention how unstable such an extended polyene would be, regardless of whether it is in a ring or not.
You might be confusing this concept with trans double bonds in a ring, or alkynes in a ring. In this case, the cut off point is about 8 carbons for both of these to have either a single trans alkene or a single alkyne, although both are less stable than if they were in a larger ring.
One interesting question would be: what is the minimum number of carbons to put even a single a cumulated diene in a ring? I don't know the answer.


Matthew P.
03/19/19
Victor K.
7 carbons. 1,2-cycloheptadiene and its derivatives are known.03/16/19