It was reported earlier [Phys. Rev. Lett. 106, 056401 (2011)] that the skutterudite structure compound CoSb3 displays a unique band structure with a topological transition versus a symmetrypreserving 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 3 site symmetry, and with its lack of moment. The Sb states are characterized as px (separately, py) σ-bonded Sb4 ring states occupied and the corresponding antibonding states empty. The remaining (locally) pz 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 A2u 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.