In the intriguing Ba5Ga6 phase of Fornasini and Pani, one finds isolated, nearly perfect octahedral Ga-6 clusters with one more skeletal electron pair (i.e., Ga-6(10-)) than predicted by the Wade-Mingos rules. The electronic structures of the molecular Ga octahedron and Ba5Ga6 were studied by the extended Huckel method. According to our calculations, the octahedral cluster, either as isolated Ga-6(10-) or in the extended Ba5Ga6 structure, appears to be unstable with respect to Jahn-Teller distortion. There is room for hydrides in the Ba5Ga6 structure; Ba5Ga6H2 is an attractive formulation, for it should have, as our computations indicate, relatively undistorted Ga-6 octahedra in it.