High yields of the novel BaHg2Tl2 are achieved from reactions of the appropriate cast alloys at similar to 400 degrees C. (Isotypic SrHg2Tl2 also exists.) The tetragonal barium structure (P4(2)/mnm, a = 10.606 angstrom, c = 5.159 angstrom) was refined from both single-crystal X-ray and neutron powder diffraction data in order to ensure the atom site assignments although distances and calculated atom site population also support the results. The Hg and Tl network atoms are distinctive in their functions and bonding. Parallel chains of Hg hexagons and of Tl tetrahedra along care constructed from polyhedra that share opposed like edges, and these are in turn interconnected by Hg-Tl bonds. Overall, the number of Tl-Tl bonds per cell exceeds the Hg-Hg type by 20:12, but these are similar to 1:2 each in bonding according to their average -ICOHP values (related to overlap populations). Barium is bound within a close 15-atom polyhedron, 12 atoms of which are the more electronegative Hg. LMTO-ASA calculations show that scalar relativistic effects are particularly important for Hg 5d-6s mixing in Hg-Hg and Hg-Tl bonding, whereas relatively separate Tl 6s and 6p states are more important in Tl-Tl interactions. The 6p states of Hg and Tl and 5d of Ba define a dominant conduction band around E-F, and the phase is metallic and Pauli-like paramagnetic. The thallium characteristics here are close to those in numerous alkali-metal-Ti cluster systems. Other active metal-mercury phases that have been studied theoretically are all distinctly electron-richer and more reduced, and without appreciable net 5d, 6s contributions to Hg-Hg bonding.