  Recent results of Hassett, Kuznetsov and others pointed out countably many
divisors $C_d$ in the open subset of
$\mathbb{P}^{55}=\mathbb{P}(H^0(\mathcal{O}_{\mathbb{P}^5}(3)))$ parametrizing
all cubic 4-folds and lead to the conjecture that the cubics corresponding to
these divisors should be precisely the rational ones. Rationality has been
proved by Fano for the first divisor $C_{14}$ and in [arXiv:1707.00999] for the
divisors $C_{26}$ and $C_{38}$. In this note we describe explicit birational
maps from a general cubic fourfold in $C_{14}$, in $C_{26}$ and in $C_{38}$ to
$\mathbb{P}^4$, providing concrete geometric realizations of the more abstract
constructions in [arXiv:1707.00999].
