Hollandite (α-)MnO2 gives superior performance compared to other MnO2 polymorphs in surface sensitive applications in supercapacitors and catalysis. However, a thorough understanding of its atomic-scale surface properties is lacking, which we address here using density functional theory (DFT). A Wulff construction based upon relaxed surface energies demonstrates that the equilibrium morphology expresses the low index (100), (110) and (111) surfaces as well as the high index (211) and (112) surfaces. The predicted morphology exhibits clear elongation along the c-axis which is consistent with the large number of nanorod type structures that are obtainable experimentally. The surface structures expressed in the morphology are discussed in detail and it is found that α-MnO2 gives rise to larger surface relaxations than are observed for the less open rutile structured MnO2. Enhanced magnetic moments at surface sites are rationalised by a crystal field argument. Experimental studies consistently find that α-MnO2 has higher catalytic activity than other polymorphs of MnO. In this work, calculated formation energies for oxygen vacancy defects at the expressed surfaces are demonstrably lower, by ∼1 eV, than for rutile MnO2 surfaces [Tompsett et al., JACS, 2014, 136, 1418]. The lowest vacancy formation energy occurs at the (112) surface, which despite its relative high Miller index constitutes 17% of the surface area of the calculated morphology. This may play a key role in the favourable catalytic performance observed for α-MnO2 in a broad range of applications.