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Neutral counting assigns five electrons to cyclopentadienyl ligand and two to CO. Thus each $\mathrm{FeCpCO}$ fragment has $8+5+2=15$ valence electrons and contributes three skeletal electrons; each $\mathrm{CoCpCO}$ fragment has sixteen and contributes four:For A the six-pair four-vertex count is the nido count derived from a five-vertex trigonal bipyramid. Removing an axial vertex leaves a tetrahedron: the three equatorial vertices plus the remaining axial vertex. For B the corresponding arachno fragment is obtained by removing both axial vertices from that same parent, leaving a three-metal triangle. Small clusters require specifying the parent and removed vertices; mechanically calling every nido fragment a square pyramid is wrong.

The Fe tetramer is indeed known to have a tetrahedral $\mathrm{F}{\mathrm{e}}_4$ core, with four face-capping CO groups. The carbon atoms of those carbonyls and the iron atoms form interpenetrating tetrahedra, giving a cubane-like Fe–C connectivity. Bridging rather than terminal CO changes the distribution of local donation, not the total electron count above.^[ref]

Place the trigonal axis along $z$, the axial ligands on $\pm z$ and the equatorial ligands in the $xy$ plane. The ordering is $e^{\prime \prime }(d_{xz},d_{yz})<e^{\prime }(d_{xy},d_{x^2-y^2})<a_1^{\prime }(d_{z^2})$. The $e^{\prime \prime }$ pair has nodal behaviour along both the equatorial ligand directions and the axial axis, minimizing direct ligand repulsion. The in-plane $e^{\prime }$ pair points into the equatorial region. The $d_{z^2}$ lobes point at both axial ligands and its torus also samples the equatorial ligands, giving the largest repulsion in the regular point-charge geometry.

Rotation by 120° and reflection in the equatorial plane preserve the geometry; they enforce the indicated doublet degeneracies. The ordering concerns a regular trigonal bipyramid with equivalent ligand-field assumptions, not every distorted five-coordinate complex.