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We recall that a smooth ample surface $\mathcal{S}$ in a general$(1,2,2)$-polarized abelian threefold, which is the pullback of the Thetadivisor of a smooth plane quartic curve $\mathcal{D}$, is a surface isogenousto the product $\mathcal{C} \times \mathcal{C}$, where $\mathcal{C}$ is a genus$9$ curve embedded in $\mathbb{P}^3$ as complete intersection of a smoothquadric and a smooth quartic. We show that the space of global holomorhicsections of the canonical bundle of this surface is generated by certaindeterminantal bihomogeneous polynomials of bidegree $(2,2)$ on $\mathbb{P}^3$,which can be used to define biquadratic addition laws on the Jacobi model ofelliptic curves, embedded in $\mathbb{P}^3$ as complete intersection of twoquadrics. Finally, we use this interesting relationship with the biquadraticaddition laws to describe the behavior of the canonical map of $\mathcal{S}$.

Biquadratic addition laws on elliptic curves in $\mathbb{P}^3$ and the canonical map of the $(1,2,2)$-Theta divisor