> Getting every degree from 3 to n/2 without leaving rotation symmetry is a surprisingly wide family. Not really wide in the sense that matters, the constructions are only on the very sparse lengths 30·7^j and 70t, so this is more a neat existence result than a broad family. The degree range is full, sure, but the ambient n restriction does most of the work here.

Only a sparse infinite family, not every even n, so the real restriction is on length, not degree.