  We introduce and study tetrahedron instantons, which can be realized in
string theory by D$1$-branes probing a configuration of intersecting
D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they
capture instantons on $\mathbb{C}^{3}$ in the presence of the most general
intersecting real codimension-two supersymmetric defects. Moreover, we
construct the tetrahedron instantons as particular solutions of general
instanton equations in noncommutative field theory. We analyze the moduli space
of tetrahedron instantons and discuss the geometric interpretations. We compute
the instanton partition function both via the equivariant localization on the
moduli space of tetrahedron instantons and via the elliptic genus of the
worldvolume theory on the D$1$-branes probing the intersecting D$7$-branes,
obtaining the same result. The instanton partition function of the tetrahedron
instantons lies between the higher-rank Donaldson-Thomas invariants on
$\mathbb{C}^{3}$ and the partition function of the magnificent four model,
which is conjectured to be the mother of all instanton partition functions.
Finally, we show that the instanton partition function admits a free field
representation, suggesting the existence of a novel kind of symmetry which acts
on the cohomology of the moduli spaces of tetrahedron instantons.
