  The ground-state properties of spin polarized hydrogen H$\downarrow$ are
obtained by means of diffusion Monte Carlo calculations. Using the most
accurate to date ab initio H$\downarrow$-H$\downarrow$ interatomic potential we
have studied its gas phase, from the very dilute regime until densities above
its freezing point. At very small densities, the equation of state of the gas
is very well described in terms of the gas parameter $\rho a^3$, with $a$ the
s-wave scattering length. The solid phase has also been studied up to high
pressures. The gas-solid phase transition occurs at a pressure of 173 bar, a
much higher value than suggested by previous approximate descriptions.
