  Motivated by the recent interest in Lie algebraic and geometric structures
arising from tensor products of division algebras and their relevance to high
energy theoretical physics, we analyze generalized bioctonionic projective and
hyperbolic planes. After giving a Veronese representation of the
complexification of the Cayley plane $\mathbb{O}P_{\mathbb{C}}^{2}$, we present
a novel, explicit construction of the bioctonionic Cayley-Rosenfeld plane
$\left( \mathbb{C}\otimes \mathbb{O}\right) P^{2}$, again by exploiting
Veronese coordinates. We discuss the isometry groups of all generalized
bioctonionic planes, recovering all complex and real forms of the exceptional
groups $F_{4}$ and $E_{6}$, and characterizing such planes as symmetric and
Hermitian symmetric spaces. We conclude by discussing some possible physical
applications.
