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The electric quadrupole-quadrupole (Eqq) interaction is believed to play an important role in the broken symmetry transition from Phase I to II in solid hydrogen. To evaluate this, we study structures adopted by purely classical quadrupoles using Markov Chain Monte Carlo simulations of fcc and hcp quadrupolar lattices. Both undergo rst-order phase transitions from rotationally ordered to disordered structures, as indicated by a discontinuity in both quadrupole interaction energy (Eqq) and its heat capacity. Cooling fcc reliably induced a transition to the Pa3 structure, whereas cooling hcp gave inconsistent, frustrated and c=a-ratio-dependent broken symmetry states. Analysing the lowest-energy hcp states using simulated annealing, we found P63=m and Pca21structures found previously as minimum-energy structures in full electronic structure calculations. The candidate structures for hydrogen Phases III-V were not observed. This demonstrates that Eqq is the dominant interaction determining the symmetry breaking in Phase II. The disorder transition occurs at signicantly lower temperature in hcp than fcc, showing that the Eqq cannot be responsible for hydrogen Phase II being based on hcp.