Polymer hexosomes are block copolymer solution morphologies that adopt an internal structure composed of an inverse hexagonal (HII) phase. To date, most polymer hexosomes are reportedly rotationally symmetric solid structures that possess a common feature where hexagonally ordered inverted cylinders rotate along a central axis of symmetry to form circular hoops. Here, we report on the formation of polymer hexosomes whose inverted cylinders orient in an unusual manner, forming hoops that are noncircular. For topological reasons, this led to the generation of four defects in the resulting hexosome structure. We find that these defect-bearing hexosomes are hollow, thereby resembling polymer vesicles or polymersomes with an inverse hexagonal cylindrical morphology in the shell. The topological defects of these so-called "vesicular hexosomes" are enticing as they could serve as a platform to spatially anchor targeting ligands or biomolecules on the surface, while the hollow cylindrical shell and the vesicular lumen could spatially accommodate cargoes within the different domains. We propose that these vesicular hexosomes do not form via a conventional nucleation-growth self-assembly pathway, but rather via a two-step process involving first liquid-liquid phase separation followed by polymer microphase separation.