= Solution
For the <tetrahedral symmetry> classes $(E,8C_3,3C_2,6S_4,6\sigma_d)$, each set of four $s$ <atomic orbitals> has
$$
\boxed{\chi_{\rm Li}=\chi_{\rm Na}=(4,1,0,0,2).}
$$
The counts are the fixed sites of each <symmetry operation>: a threefold rotation fixes one vertex of each tetrahedron, a twofold or improper fourfold operation fixes none, and a diagonal mirror fixes two. <Character orthogonality> reduces each set to
$$
\boxed{\Gamma_{\rm Li}=\Gamma_{\rm Na}=A_1\oplus T_2.}
$$
The dimensions $1+3=4$ provide a check. Thus the complete eight-orbital model contains two copies of each of $A_1$ and $T_2$, which can mix across the two species.
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