The preparation, isolation, and structural/bonding characterization of four high-nuclearity neutral homopalladium clusters, Pd-16(CO)(13)(PMe3)(9) 1, Pd-35(CO)(23)(PMe3)(15) 2, Pd-39(CO)(23)(pMe(3))(16) 3 and Pd-59(CO)(32)(PMe3)(21), 4, and a minor bimetallic product, Pd29Ni3(CO)(22)(PMe3)(13) 5, are given. The four homopalladium clusters were characterized by CCD X-ray crystallographic determinations, elemental analyses, IR, multinuclear NMR, and cyclic voltammetry; because 5 was obtained in very low yields, both its molecular geometry and composition were established from the X-ray crystallographic analysis. These five clusters, obtained from reactions of a cep Pd-Ni carbonyl cluster precursor and PMe3 (with or without acetic acid), exhibit five different types (four unprecedented) of centered icosahedral-based transition-metal frameworks: (1) the Pd-16 core in 1 possesses a centered Pd-13 icosahedron. (2) The Pd-35 and Pd-39 core's in 2 and 3 each have a face-fused centered Pd-23 biicosahedron with linear (pseudo-D-3h) and bent (pseudo-C-2v) geometries, respectively; the pseudo-D-3h central Pd-29 polyhedron of the Pd-35 core in 2 approximately conforms to five interpenetrating centered icosahedra. (3) The crystallographic-D-3 (32) Pd-59 core in 4 has two centered Pd-13 icosahedra that are indirectly connected via trans double face-sharing with an inner face-fused Pd-9 bioctahedron; the entire nanosized face-condensed Pd-59 core has 11 interior Pd(i) atoms. (4) The Pd29Ni3 core in 5 contains a pseudo-T-d central Pd, polyhedron comprised of four interpenetrating centered icosahedra. The existence of these highly condensed icosahedral-based metal carbonyl clusters, found only for Pd but not for the other eight Group 8-10 transition metals, may be ascribed to Pd metal having the weakest metal-metal bonding (i.e., smallest cohesive energy). Electronic closed-shell stabilization of each of these clusters is indicated by electron-counting condensation rules giving calculated values in exact agreement with observed electron counts for the metal cores in 1, 2, 4, and 5 (i.e., irregular condensations prevent a reliable electron count in 3). Proposed growth sequences provide logical pathways in the formation of the central palladium fragments in 2, 3, 4 and 5 from the centered Pd-13 icosahedral fragment in 1.