  A new method is introduced to simulate jamming of polyhedral grains under
controlled stress that incorporates global degrees of freedom through the
metric tensor of a periodic cell containing grains. Jamming under
hydrostatic/isotropic stress and athermal conditions leads to a precise
definition of the ideal jamming point at zero shear stress. The structures of
tetrahedra jammed hydrostatically exhibit less translational order and lower
jamming-point density than previously described `maximally random jammed' hard
tetrahedra. Under the same conditions, cubes jam with negligible nematic order.
Grains with octahedral symmetry jam in the large-system limit with an abundance
of face-face contacts in the absence of nematic order. For sufficiently large
face-face contact number, percolating clusters form that span the entire
simulation box. The response of hydrostatically jammed tetrahedra and cubes to
shear-stress perturbation is also demonstrated with the variable-cell method.
