  We report the crystal structure of a new polymorph of Ca$_3$P$_2$, and an
analysis of its electronic structure. The crystal structure was determined
through Rietveld refinements of powder synchrotron x-ray diffraction data.
Ca$_3$P$_2$ is found to be a variant of the Mn$_5$Si$_3$ structure type, with a
Ca ion deficiency compared to the ideal 5:3 stoichiometry to yield a
charge-balanced compound. We also report the observation of a secondary phase,
Ca$_5$P$_3$H, in which the Ca and P sites are fully occupied and the presence
of interstitial hydride ions creates a closed-shell electron-precise compound.
We show via electronic structure calculations of Ca$_3$P$_2$ that the compound
is stabilized by a gap in the density of states compared to the hypothetical
compound Ca$_5$P$_3$. Moreover, the calculated band structure of Ca$_3$P$_2$
indicates that it should be a three-dimensional Dirac semimetal with a highly
unusual ring of Dirac nodes at the Fermi level. The Dirac states are protected
against gap opening by a mirror plane in a manner analogous to graphene. The
results suggest that further study of the electronic properties of Ca$_3$P$_2$
will be of interest.
