  We construct a new family of entire solutions to the Yamabe equation
$$-\Delta u=\frac{n(n-2)}{4}|u|^{\frac{4}{n-2}}u \mbox{ in
}\mathcal{D}^{1,2}(\mathbb{R}^n).$$ If $n=3$, our solutions have maximal rank,
being the first example in odd dimension. Our construction has analogies with
the doubling of the equatorial spheres in the construction of minimal surfaces
in $S^3(1)$.
