A series of quaternary sulfides of the composition Na3MGaS4 (M = Mn (1), Fe (2), and Co (3)) have been synthesized in sealed quartz ampules. In these compounds, divalent transition metal and Ga occupy the same crystallographic site in the Ga-S network, forming a supertetrahedral, T2 (adamantane) unit, through the corner sharing of four M/GaS4 tetrahedra. The corner sulfur atoms of the T2 clusters are further connected to similar T2 units to form an open continuous three-dimensional (3D) anionic framework of composition {[Ga2M2S8](n)}(6-). The framework resembles a zinc blende structure type if each T2 cluster is considered as a single tetrahedron and two such frameworks are intertwined to generate channels wherein reside the extra-framework Nal(+) ions. Placement of transition metals (Mn or Fe or Co) in the corner of a perfect supertetrahedron, adamantane building unit, generates an ideal lattice for geometrical magnetic frustration, which, on dilution with nonmagnetic metal (Ga), creates an ideal case for random frustration. Preliminary magnetic measurements indicate high negative values of the Weiss constant (-200 to -400 K) and the absence of any magnetic ordering, reinforcing the presence of magnetic frustration in all of these compounds.