  Monte Carlo simulations are performed to determine the critical percolation
threshold for interpenetrating square objects in two dimensions and cubic
objects in three dimensions. Simulations are performed for two cases: (i)
objects whose edges are aligned parallel to one another and (ii) randomly
oriented objects. For squares whose edges are aligned, the critical area
fraction at the percolation threshold phi_c=0.6666 +/- 0.0004, while for
randomly oriented squares phi_c=0.6254 +/- 0.0002, 6% smaller. For cubes whose
edges are aligned, the critical volume fraction at the percolation threshold
phi_c=0.2773 +/- 0.0002, while for randomly oriented cubes phi_c=0.2236 +/-
0.0002, 24% smaller.
