  We present a generalization of a family of points on $\mathbb{S}^2$, the
Diamond ensemble, containing collections of $N$ points on $\mathbb{S}^2$ with
very small logarithmic energy for all $N\in\mathbb{N}$. We extend this
construction to the real projective plane $\mathbb{RP}^2$ and we obtain upper
and lower bounds with explicit constants for the Green and logarithmic energy
on this last space.
