The notion of basic net (called also basic polyhedron) on $S^2$ plays a central role
in Conway's approach to enumeration of knots and links in $S^3$.
Drobotukhina applied this approach for links in $\RP^3$ using basic nets on $\RP^2$.
By a result of Nakamoto, all basic nets on $S^2$ can be obtained
from a very explicit family of minimal basic nets (the nets $(2\times n)^*$, $n\ge3$,
in Conway's notation) by two local transformations.
We prove a similar result for basic nets in $\RP^2$.

We prove also that a graph on $\RP^2$ is uniquely determined by its
pull-back on $S^3$ (the proof is based on Lefschetz fix point theorem).