A D20 (dice) has sides where $N-1,N,N+1$ are always neighbours on surface of solid. For which DN is this possible?

Question

A regular gon D20 dice used for example in various forms of gambling and trading card games is shown below

As can be seen each number $N$ residing on some face has two of it's neighbouring faces with numbers $N-1$ and $N+1$. Can we prove somehow for which regular N-gons this is possible to do?