  It was reported earlier [Phys. Rev. Lett. 106, 056401 (2011)] that the
skutterudite structure compound CoSb$_3$ displays a unique band structure with
a topological transition versus a symmetry-preserving sublattice (Sb)
displacement very near the structural ground state. The transition is through a
massless Dirac-Weyl semimetal, point Fermi surface phase which is unique in
that (1) it appears in a three dimensional crystal, (2) the band critical point
occurs at $k$=0, and (3) linear bands are degenerate with conventional
(massive) bands at the critical point (before inclusion of spin-orbit
coupling). Further interest arises because the critical point separates a
conventional (trivial) phase from a topological phase. In the native cubic
structure this is a zero-gap topological semimetal; we show how spin-orbit
coupling and uniaxial strain converts the system to a topological insulator
(TI). We also analyze the origin of the linear band in this class of materials,
which is the characteristic that makes them potentially useful in
thermoelectric applications or possibly as transparent conductors. We
characterize the formal charge as Co$^{+}$ $d^8$, consistent with the gap, with
its $\bar{3}$ site symmetry, and with its lack of moment. The Sb states are
characterized as $p_x$ (separately, $p_y$) $\sigma$-bonded $Sb_4$ ring states
occupied and the corresponding antibonding states empty. The remaining
(locally) $p_z$ orbitals form molecular orbitals with definite parity centered
on the empty $2a$ site in the skutterudite structure. Eight such orbitals must
be occupied; the one giving the linear band is an odd orbital singlet $A_{2u}$
at the zone center. We observe that the provocative linearity of the band
within the gap is a consequence of the aforementioned near-degeneracy, which is
also responsible for the small band gap.
