Abstract: Tetrahedron instantons were recently introduced by Pomoni-Yan-Zhang in string theory, as a way to describe systems of D0-D6 branes with defects. We propose a rigorous geometric interpretation of their work by the point of view of Donaldson-Thomas theory. We will explain how to naturally construct the moduli space of tetrahedron instantons as a Quot scheme, parametrizing quotients of a torsion sheaf over a certain singular threefold, and how to construct a virtual fundamental class in this setting using quiver representations and the recent machinery of Oh-Thomas (which is in principle designed for moduli spaces of sheaves on Calabi-Yau 4-folds). Furthermore, we will show how to formalize mathematically the invariants considered by Pomoni-Yan-Zhang (initially defined via supersymmetric localization in Physics) and how to rigorously compute them, solving some open conjectures. Joint work with Nadir Fasola.