The hexagonally perforated layer (HPL) phase in a polystyrene-b-poly(ethylene oxide) (PS-b-PEO) diblock copolymer was systematically studied by small-angle X-ray scattering (SAXS) in reciprocal space and transmission electron microscopy (TEM) in real space. Detailed crystallographic analyses revealed that the shear-induced, "single-crystal"-like HPL phase in the PS-b-PEO diblock copolymer sample contained a mixture of trigonal twins (similar to80%) and hexagonal (similar to20%) structures. Both structures had the same orientation and the same in-plane unit cell parameters (alpha and alpha) but different out-of-plane (c-axis) dimensions, because the trigonal structure was constructed by three layers (ABC) and the hexagonal structure had two layers (AB). Computer-simulated diffraction and TEM results implied that the correlation length of the trigonal structure along the [001] direction was relatively large (at least over 20 layers, i.e., greater than or equal tosimilar to400 nm) while that of the hexagonal structure was relatively small. The formation mechanism of the HPL phase was investigated by TEM. Various edge dislocations formed by "plastic deformation" under a large-amplitude mechanical shear were the cause of the trigonal twins and the hexagonal structure. Low-frequency rheological studies indicated that the HPL phase was metastable, and it transformed into a more stable double gyroid phase when the temperature exceeded 160 degreesC. The HPL structure reappeared after the sample was again subjected to the large-amplitude mechanical shear. Furthermore, the transformation from the HPL phase to the DG phase was also studied. It was found that the perforations of the hexagonal structure rearranged themselves first, followed by the perforations in the trigonal structure.