SrSn 2 Ga 1.3 Cr 2.7 O 11 is shown to be a strongly geometrically frustrated magnet through measurement of its temperature-dependent magnetic susceptibility and specific heat. This material, determined by powder neutron diffraction to have an R-type ferrite crystal structure, has S =3/ 2 Cr 3+ ions in isolated Kagomé planes with no magnetic ions in the intermediary structural layers. The Kagomé planes contain 10% nonmagnetic Ga 3+ . This structure type makes the chromate family of frustrated magnets unusual because it displays four spinel-based structural variants with the same basic magnetic lattice and different effective dimensionalities and degrees of frustration. A comparison of the structures and magnetic characteristics is presented.