  Complex tetrahedral surface $\mathcal{T}$ is a non planar projective surface
that is generated by four intersecting complex projective planes $CP^{2}$. In
this paper, we study the family $\{\mathcal{T}_{m}\} $ of blow ups of
$\mathcal{T}$ and exhibit the link of these $\mathcal{T}_{m}$s with the set of
del Pezzo surfaces $dP_{n}$ obtained by blowing up n isolated points in the
$CP^{2}$. The $\mathcal{T}_{m}$s are toric surfaces exhibiting a $U(1) \times
U(1) $ symmetry that may be used to engineer gauge symmetry enhancements in the
Beasley-Heckman-Vafa theory. The blown ups of the tetrahedron have toric graphs
with faces, edges and vertices where may localize respectively fields in
adjoint representations, chiral matter and Yukawa tri-fields couplings needed
for the engineering of F- theory GUT models building.
