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Polyethylene forms a two-dimensional hexagonal phase, stable at 3 GPa depending on molecular length, which in recent years has been claimed to intervene in crystallization prior to the formation of the usual orthorhombic phase even at atmospheric pressure. This claim is evaluated and shown to be without substance. There is very little evidence that the theoretical possibility of thin lamellae being more stable in the hexagonal phase than the orthorhombic at atmospheric pressure, if the former has sufficiently low fold surface free energy, does occur in practice. But the existence of single crystals of the orthorhombic phase unambiguously shows that they did not have a hexagonal precursor; that would have made them threefold twins. The overwhelming mass of evidence is that orthorhombic and hexagonal phases crystallize independently in accordance with the phase diagram and kinetic competition during growth, as has been understood since the hexagonal phase was discovered.