 Solution

A shell with angular momentum $l$ holds $2(2l+1)$ electrons. Successively filling the shells listed in the source gives the closed-shell totalsFor $\mathrm{A}{\mathrm{l}}_4\mathrm{C}{\mathrm{p}}_4^{\ast }$ the delocalized count is $4(3)-4=8$, matching $1S^{2}1P^6$. 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.