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Aspects of plastic anisotropy in damage accumulation are considered for a class of hexagonal crystals that deform by combined slip and twinning. Focus is placed on crystallographic aspects that are currently absent from constitutive formulations of ductile damage. To this end, three-dimensional finite-element calculations are carried out using a cubic unit cell containing a single void embedded in a crystal matrix. Plastic flow in the latter is described using crystal plasticity with parameters representative of single crystal pure magnesium. The effect of void oblateness is analyzed in some detail, as voids often form as blunted microcracks in Mg alloys. The analyses reveal two aspects peculiar to twinning-mediated void growth: (1) insensitivity of the effective stress-strain response to void oblateless and (2) a plastic auxetic effect. Both aspects manifest under certain circumstances. Some implications in terms of incorporating the uncovered crystallographic aspects in coupled plasticity-damage formulations of anisotropic materials are discussed.