= Solution
A shell with angular momentum $l$ holds $2(2l+1)$ electrons. Successively filling the shells listed in the source gives the closed-shell totals
$$
\boxed{2,8,18,20,34,40,58,68,90,92,106,112,138.}
$$
For $\mathrm{Al_4Cp^*_4}$ the delocalized count is \b[$4(3)-4=8$], matching $1S^21P^6$. The tetrahedral aluminium core is consequently consistent with the <jellium model>. Counting the same eight electrons as though the tetrahedron were an ordinary closo Wade cluster would fail: a four-vertex closo framework would require $2n+2=10$ skeletal electrons. The competing models use different physical assumptions and should not be interchanged just because both involve a polyhedron.
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