Group 13-15 binary hydrides, [HMYH] n , together with their substituted analogues, hold the promise for acting as precursors for group 13-15 semiconducting nanomaterials. [1,2] Structural characteristics of the higher oligomeric cages of the hydrides are known to differ from their valence isoelectronic carbon analogues. The combination of 12 five-membered rings and a variable number of six-membered rings, [3] familiar from fullerenes [4] and carbon nanotubes, [5] does not apply, since the five-membered rings would require the presence of MÀM and YÀY bonds. This structural problem can be avoided by replacing the 12 pentagons with six squares, as postulated for boron nitride cages.[6] Previous theoretical studies on [HMYH] n structures where n 16, have led to the conclusion that needleshaped structures with three adjacent squares at each end are thermodynamically favored for all group 13-15 pairs. [7,8] Very recently, the existence of perhydrogenated fullerenes, that is, the fulleranes, has been predicted, where partial endo-hydrogenation significantly stabilizes the cages.[9] In the theoretical study reported herein, we demonstrate that application of the structural motifs of the fulleranes for group 13-15 binary hydrides produces stable "in-out" isomeric cages without adjacent squares.We compared the needle-shaped structures with tetrahedral cages for group 13-15 binary hydrides [HMYH] n , (M= B, Al, Ga; Y = N, P, As). The curvature of the cages flattens as a function of the size of the cage, making large exo-hydrogenated cage structures unfavorable due to distortion from the optimal sp 3 hybridization. The problem with large structures can be overcome by partial endo-hydrogenation, which has been demonstrated to produce very stable C 80 H 80 and C 180 H 180 fulleranes with stabilities improving as a function of the size of the cage.[9] This "in-out" isomerism originates from puckering of the hexagons and hence applies for group 13-15 binary hydrides, as well. Since the six squares, necessary for cage closure, cannot participate in the puckering, the "in-out" isomerism requires the presence of atoms that are not a part of a square. The smallest tetrahedral cage meeting the requirement is the T d -symmetric [HMYH] 16 (Figure 1 a). Here, the atoms that basically could become endo-hydrogenated are the four connecting each set of three squares. Due to its small size, however, the repulsions between the endo-hydrogens would destabilize the cage. The next tetrahedral cage in the series is the Tsymmetric [HMYH] 28 , which already has sufficient space for endo-hydrogenation. A particularly favorable species is obtained by endo-hydrogenation of every other atom at the distance of two MÀY bonds from each square atom (Figure 1 b).We optimized the compounds shown in Figure 1 at the B3LYP/TZVP level of theory. The stabilities of the cages compared to the isomeric needles (Figures 1 c-1 d) are given in Figure 2, showing total energies and Gibbs free energies (T = 298.15 K) per HMYH unit relative to the previously reported...