<jats:title>Abstract</jats:title><jats:p>In this study, the three-dimensional (3-D) microstructure of polar firn is investigated by means of X-ray microfocus computer tomography (mCT). Basic topological properties including the Euler and coordination numbers are derived from the reconstructed 3-D volume images. It is shown that sample volumes of about 4 cm<jats:sup>3</jats:sup> are representative for polar firn in terms of their connectivity. The connectivity function defined as the change of Euler number with structure size is calculated via image-processing routines. It is used to split the ice phase at small bridges into single crystallite agglomerates. The bond-size distributions and the mean size of the agglomerates are estimated. All μCT measurements were carried out on the uppermost 9 m of a shallow firn core (B35) drilled during the 2005/06 field campaign at Kohnen station, Dronning Maud Land (DML), Antarctica. The results are compared with estimates from classical two-dimensional (2-D) surface section observations. The 3-D approach confirms the linear relationship between coordination number and density which hitherto has only been derived from 2-D observations. Layers of buried snow dunes show a stronger connectivity than layers of moderate crystal size and density. The formation of agglomerates made of crystallites is a common feature of polar firn in DML. It is proposed that the growth of agglomerates leads to reduced critical densities for the transition between the densification regime of grain boundary sliding and plastic deformation.</jats:p>