Single crystals of a new iron-containing oxide, Ba4KFe3O9, were grown from a hydroxide melt, and the crystal structure was determined by single-crystal X-ray diffraction. This ferrite represents the first complex oxide containing isolated 6-membered rings of corner-sharing FeO4 tetrahedra. Mossbauer measurements are indicative of two tetrahedral high-spin Fe3+ coordination environments. The observed magnetic moment (similar to 3.9 mu(B)) at 400 K is significantly lower than the calculated spin-only (similar to 5.2 mu(B)) value, indicating the presence of strong antiferromagnetic interactions in the oxide. Our density functional theory calculations confirm the strong antiferromagnetic coupling between adjacent Fe3+ sites within each 6-membered ring and estimate the nearest-neighbor spin-exchange integral as similar to 200 K; next-nearest-neighbor interactions are shown to be negligible. The lower than expected effective magnetic moment for Ba4KFe3O9 calculated from chi T data is explained as resulting from the occupation of lower-lying magnetic states in which more spins are paired. X-band (9.5 GHz) electron paramagnetic resonance (EPR) spectra of a powder sample consist of a single line at g similar to 2.01 that is characteristic of Fe3+ ions in a tetrahedral environment, thus confirming the Mossbauer results. Further analysis of the EPR line shape reveals the presence of two types of Fe-6 magnetic species with an intensity ratio of similar to 1:9. Both species have Lorentzian line shapes and indistinguishable g factors but differ in their peak-to-peak line widths (delta B-pp). The line-width ratio delta B-pp(major)delta B-pp(minor) similar to 3.6 correlates well with the ratio of the Weiss constants, theta(minor)/theta(major) similar to 4.