= Solution
For $[\mathrm{B_{12}H_{12}}]^{2-}$, twelve BH vertices supply $12(2)$ skeletal electrons and the charge adds two:
$$
N_{\rm skel}=26=2(12+1).
$$
For the <cobaltacarborane>, nine BH vertices supply 18, two CH vertices supply six and CpCo supplies two by (a):
$$
N_{\rm skel}=9(2)+2(3)+2=26.
$$
\b[Both are 12-vertex <closo> icosahedra with 13 <skeletal electron pairs>.] In the <cobalt> compound, the Cp ring is external to the cage. <cobalt> caps the five-membered open face of the 11-vertex dicarbollide fragment and is a vertex of the resulting icosahedron, giving the usual adjacent-carbon <cobaltacarborane> framework. Counting all five Cp carbons as additional polyhedral vertices would be incorrect.
\Image[/past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1-closo-icosahedra.png]
{title=Original 12-vertex closo frameworks for dodecaborate and the adjacent-carbon cobaltacarborane, with external ligands omitted}
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