Density functional theory (DFT) studies predict the dianions CpCoBn-1Hn-12- (n = 9, 10, 11, 12; Cp = eta(5)-C5H5) to have structures based on the most spherical deltahedra found in the isoelectronic boranes BnHn2-. In the CpCoB8H82- dianion the non-equivalent structures with the cobalt atom at a degree 4 vertex and at a degree 5 vertex are essentially degenerate in terms of energy (within similar to 1 kcal/mol). For the CpCoBn-1Hn-12- dianions (n = 10, 11, 12) the cobalt atom prefers energetically the vertices of the lowest possible degree (four for n= 10 and 11, five for n = 12). Structures for the neutral species CpCoBn-1Hn-1 (n = 10, 11, 12) based on isocloso deltahedra. with the cobalt atom at a degree 6 vertex are preferred energetically by 9, 19, and 53 kcal/mol, respectively, over alternative structures. However, for CpCoB8H8 the closo tricapped trigonal prismatic structure with the cobalt atom at a degree 5 vertex is energetically preferred by similar to 9 kcal/mol over the isocloso deltahedral structure with the cobalt atom at a degree 6 vertex. The lowest energy structures predicted for the dications CpCoB8H82+ and CpCoB9H92+ are highly oblate (flattened) deltahedra with the cobalt atom at a degree 7 vertex, A complicated potential energy surface was found for CpCoB10H102+ including non-deltahedral structures with a single quadrilateral or pentagonal face. The predicted lowest energy structures for both CpCoB11H11 and CpCoB11H112+ are based on the same 12-vertex deltahedron with three degree 6, six degree 5, and three degree 4 vertices, and thus topologically different from the regular icosahedron normally found in boron chemistry.