= Tetrahedral s-orbital symmetry combinations
Four equivalent $s$ <atomic orbitals> at the vertices of a regular <tetrahedron> carry the <tetrahedral symmetry> representation $A_1\oplus T_2$. The normalized equal sum is $A_1$; three coordinate-sign combinations span $T_2$. Every normalized coefficient vector has entries $\pm1/2$ in a suitable orthonormal real basis. These functions simplify a <Hamiltonian> invariant under the tetrahedral operations, but equivalent symmetry copies on other sites may still mix.
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