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-member rings of corner sharing FeO4 tetrahedra. Mössbauer measurements are indicative of two tetrahedral high-spin Fe3+ coordination environments. The observed magnetic moment (~3.9 BM) at 400 K is significantly lower than the calculated spin-only (~5.2 BM) value indicating the presence of strong antiferromagnetic interactions in the oxide. Our density functional calculations confirm the strong antiferromagnetic coupling between adjacent Fe3+ sites within each 6-member ring and estimate the nearest neighbor spin exchange integral as ~200 K; next nearest neighbor interactions are shown to be negligible. The lower than expected effective moment for Ba4KFe3O9 calculated from χT 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 powder sample consist of a single line at g~2.01 that is characteristic of Fe3+ ions in a tetrahedral environment, thus, confirming the Mössbauer results. Further analysis of the EPR line shape reveals the presence of two types of Fe6 magnetic species with an intensity ratio of ~1:9. Both species have Lorentzian line shapes and indistinguishable g-factors but differ in the peak-to-peak line widths (δBpp). The line width ratio δBpp(major)/δBpp(minor) ~ 3.6 correlates well with the ratio of the Weiss constants, θminor/θmajor ~ 4.