Four examples of R5Au2Te2 (vec = 29 e(-); R = Lu, Ho, Dy, Y) have been synthesized by high-temperature solid-state techniques, isotypic examples of Tm5Sb2Si2 (vec = 33 e(-)) and binary Eu5As4 (vec = 30 e(-)). The crystal structure was established for Lu5Au2Te2, (orthorhombic Cmce (No. 64), a = 15.056(2), b = 7.749(1), c = 7.754(1) angstrom, and Z = 4), in which pairs of tellurium layers alternate with two-dimensional (2D) Lu5Au2 slabs that are aggregated in such a way that each Au-2-centered bi-trigonal prism (BTP) of Lu interconnects four other identical units, with the remaining cavities filled by nominal body-centered Lu cubes. The metal-metal aggregation in this structure provides a novel building unit in ternary rare-earth-metal-rich tellurides. Linear-muffin-tin-orbital (LMTO) electronic structure calculations and COHP analyses reveal that Lu5Au2Te2 is a poor metal with Au-2 dimers and strong polar Lu-Au and Lu-Te interactions. The first theoretical analysis of the binary parent structure Eu5As4 (vec = 30 e(-)) provides a simpler description of the equivalent orbital interactions and a closed shell gap in terms of the idealized (Eu2+)(5)(As-2(4-))(As3-)(2) representation, particularly for the explicit filled As-2 levels sigma(s), sigma(s)*, sigma(p), pi, pi*, plus empty sigma(p)*. Crystal Orbital Hamilton Population (-COHP) data illuminate the prominent roles that polar bonding of Eu-As or Lu-Te and Lu-Au and relativistic effects with gold play in these, the former corresponding to 83% and 86% of the total Hamilton population for Eu5As4 and Lu5Au2Te2, respectively.