Additively manufactured soft magnetic Fe-3.7%w.t.Si toroidal samples with solid and novel partitioned cross-sectional geometries are characterized through magnetic measurements. This study focuses on the effect of air gaps and annealing temperature on AC core losses at the 50 Hz frequency. In addition, DC electromagnetic material properties are presented, showing comparable results to conventional and other 3D-printed, high-grade, soft magnetic materials. The magnetization of 1.5 T was achieved at 1800 A/m, exhibiting a maximum relative permeability of 28,900 and hysteresis losses of 0.61 (1 T) and 1.7 (1.5 T) W/kg. A clear trend of total core loss reduction at 50 Hz was observed in relation to the segregation of the specimen cross-sectional topology. The lowest 50 Hz total core losses were measured for the toroidal specimen with four internal air gaps annealed at 1200 degrees C, exhibiting a total core loss of 1.2 (1 T) and 5.5 (1.5 T) W/kg. This is equal to an 860% total core loss reduction at 1 T and a 510% loss reduction at 1.5 T magnetization compared to solid bulk-printed material. Based on the findings, the advantages and disadvantages of printed air-gapped material internal structures are discussed in detail.