Group theory arguments have demonstrated that a general odd-parity ord
er parameter cannot have line nodes in the presence of spin-orbit coup
ling. In this paper, it is shown that these arguments do not hold on t
he k(z) = pi/c zone face of a hexagonal close-packed lattice. In parti
cular, three of the six odd-parity representations vanish identically
on this face. This has potential relevance to the heavy fermion superc
onductor UPt3.