We present Rh2Cd15, the first binary compound in the Rh-Cd system. It is based on transition-metal embedded (Rh@Cdi(11) and Rh@Cd-12) endohedral Cd clusters: that are single- and double-capped IC10 composite icosahedra/cubes. We demonstrate the structural connections between the clusters. On the basis of the analysis of atomic interactions and electron counting, 50 electrons per Rh2Cd15 is postulated to be the boundary between bonding and antibonding interactions. This understanding is supported by electronic structure calculations showing that the electron count for Rh2Cd15 (48 electrons per Rh2Cd15) is located close to a deep pseudogap in the in the electronic density of states at 50 electrons per formula unit, which we postulate is an important factor in determining the new compound's stability.