### A symplectic representation of ${E}_{7}$

We explicitly construct a particular real form of the Lie algebra ${\U0001d522}_{7}$ in terms of symplectic matrices over the octonions, thus justifying the identifications ${\U0001d522}_{7}\cong \mathrm{\U0001d530\U0001d52d}(6,\mathbb{O})$ and, at the group level, ${E}_{7}\cong \text{Sp}(6,\mathbb{O})$. Along the way, we provide a geometric description of the minimal representation of ${\U0001d522}_{7}$ in terms of rank 3 objects called cubies.