The threefold containing the Bordiga surface of degree ten as a hyperplane section

Let be a very ample vector bundle of rank 2 on $\Bbb P^2$ with c1() = 4 and c2() = 6. Then it is proved that is the cokernel of a bundle monomorphism $\mathcal O_{\Bbb P^2}(1)^{\oplus 2}\to T_{\Bbb P^2}^{\oplus 2}$, where $T_{\Bbb P^2}$ is the tangent bundle of $\Bbb P^2$. This gives a new example of a threefold containing a Bordiga surface as a hyperplane section.