  By exploiting suitably constrained Zorn matrices, we present a new
construction of the algebra of sextonions (over the algebraically closed field
$\mathbb{C}$). This allows for an explicit construction, in terms of Jordan
pairs, of the non-semisimple Lie algebra $\mathbf{e_{7 \frac12}}$, intermediate
between $\mathbf{e_{7}}$ and $\mathbf{e_{8}}$, as well as of all Lie algebras
occurring in the sextonionic row and column of the extended Freudenthal Magic
Square.
