A new series of nonspherical and very oblate deltahedra, conveniently called the oblatocloso deltahedra, is found in dimetallaboranes among which the dirhenaboranes Cp2Re2Bn-2Hn-2 (8 <= n <= 12) are the prototypes. The D-6h hexagonal bipyramid is the first member of this series ( n) 8). However, the higher members of the series are not bipyramids but are derivable from them by a number of diamond-square-diamond processes. A viable model for the skeletal bonding in the oblatocloso dimetallaboranes can be developed if the two metal vertices, typically degree 6 or 7 vertices, are assumed each to contribute five internal orbitals rather than the three internal orbitals assumed by the Wade-Mingos rules. This leads to 2n + 4 actual skeletal electrons for an n vertex oblatocloso dimetallaborane rather than the Wadean 2n - 4 skeletal electrons. The surface bonding of an n vertex oblatocloso dimetallaborane then consists of n three-center two-electron bonds similar to that in corresponding isocloso metallaboranes thereby leaving four orbitals and four electrons for a metal - metal double bond inside the deltahedron. Removal of one or two boron vertices from oblatocloso deltahedra leads to oblatonido and oblatoarachno dimetallaboranes, respectively, having the same number of skeletal electrons as the oblatocloso deltahedra from which they are derived.