The geometries and energetics of the n-vertex polyhedral dicobaltadithiaboranes and dicobaltadiselenaboranes Cpsub.2Cosub.2Esub.2Bnsub.−4Hnsub.−4 (E = S, Se; n = 8 to 12) have been investigated via the density functional theory. Most of the lowest-energy structures in these systems are generated from the (n + 1)-vertex most spherical closo deltahedra by removal of a single vertex, leading to a tetragonal, pentagonal, or hexagonal face depending on the degree of the vertex removed. In all of these low-energy structures, the chalcogen atoms are located at the vertices of the non-triangular face. Alternatively, the central polyhedron in most of the 12-vertex structures can be derived from a Cosub.2Esub.2Bsub.8 icosahedron with adjacent chalcogen (E) vertices by breaking the E-E edge and 1 or more E-B edges to create a hexagonal face. Examples of the arachno polyhedra with two tetragonal and/or pentagonal faces derived from the removal of two vertices from isocloso deltahedra were found among the set of lowest-energy Cpsub.2Cosub.2Esub.2Bnsub.−4Hnsub.−4 (E = S, Se; n = 8 and 12) structures.