Carbometalates are a diverse family of solid state structures formed from transition metal (TM)-carbon polyanionic frameworks whose charges are balanced by rare earth (RE) cations. Remarkable structural features, such as transition metal clusters, are often encountered in these phases, and a pressing challenge is to explain how such features emerge from the competing interaction types (RE-M, TM-TM, TM-C, etc.) in these systems. In this Article, we describe a joint experimental and theoretical investigation of two compounds, Gd13Fe10C13 and its oxycarbide Gd13Fe10C13-xOx (x approximate to 1), which add a new dimension to the structural chemistry of carbometalates: pi-conjugation through both TM-C and TM-TM multiple bonds. The crystal structures of both compounds are built from layers of Fe-centered Gd prisms stacked along c and surrounded by an Fe-C network, and differ chiefly in the stacking sequence of these layers. The phases' identical local structures have two types of Fe environment: trigonal planar FeC3 sites and H-shaped Fe2C4 sites, with unusually short Fe-Fe and Fe-C bonds. Fe-57 Mossbauer spectroscopy and DFT-calibrated Huckel calculations on Gd13Fe10C13 build a picture of covalent Fe-C sigma bonds and conjugated pi systems for which Lewis structures can be drawn. Using the reversed approximation Molecular Orbital approach, we can draw isolobal analogies between the Fe centers of this compound and molecular TM complexes: 18-electron configurations could be achieved through sigma and pi bonds with 18 electrons/Fe for the FeC3 site and 18-n (n = 2 for an Fe=Fe double bond) electrons/Fe for the Fe2C4 site. In this way, the vision of a unified bonding scheme of carbometalates and organometallics proffered by earlier studies is realized in a visual manner, directly from the 1-electron wave functions of the Huckel model. The bonding analysis predicts that Gd13Fe10C13 is one electron/formula unit short of an ideal electron count, explaining the tendency of the system toward a small degree of oxygen substitution. Analogies between the pi bonding in Gd13Fe10C13 and that of the allyl anion help rationalize the presence of trigonal planar Fe and linear C units in the structure. The isolobal analogy between Gd13Fe10C13 and an 18-electron coordination complex is expected to apply to carbometalates as a whole, and will be extended to other examples in our future work.