  Group theory arguments have demonstrated that a general odd parity order
parameter cannot have line nodes in the presence of spin-orbit coupling. In
this paper, it is shown that these arguments do not hold on the $k_z = \pi/c$
zone face of a hexagonal close packed lattice. In particular, three of the six
odd parity representations vanish identically on this face. This has potential
relevance to the heavy fermion superconductor $UPt_3$.
