  The two-dimensional (2D) metal PtCoO$_2$ is renowned for the lowest room
temperature resistivity among all oxides, close to that of the top two
materials Ag and Cu. In addition, we theoretically predict a strong intrinsic
spin Hall effect. This originates from six strongly-tilted Dirac cones that we
find in the electronic structure near the Fermi surface, where a gap is opened
by large spin-orbit coupling (SOC). This is underpinned by rich topological
properties; in particular, the phenomenology of a mirror Chern metal is
realized not exactly, but very accurately, on account of an approximate
crystalline symmetry. We expect that such 'vicinity topology' to be a feature
of relevance well beyond this material. Our Wilson loop analysis indicates
further elaborate features such as fragile topology. These findings highlight
PtCoO$_2$ as a promising material for spintronic applications as well as a
platform to study the interplay of symmetry and topology.
