The structure–property relationships of solid solutions within the YbFe₂O₄ family of compounds have been studied in relation to their optical, dielectric and magnetic properties. This family of compounds is of recent interest because of the trigonal bipyramid coordination that is rarely observed in transition metal oxides. The systematic study of InM³⁺M²⁺O₄ (M³⁺ = Al, Fe, Ga; M²⁺ = Cu, Mg) allowed for the trigonal bipyramidal site to be analyzed based on ionic radii, electron configurations and electronegativity differences. The solid solutions of InM³⁺Cu[subscript 1-x]MgxO₄ (M³⁺ = Al, Fe, Ga) exhibited a large increase in the c lattice parameter as a result of the difference in ionic behavior between Cu²⁺ and Mg²⁺. This structural observation was not present for InGa[subscript 1-x]Fe[subscript x]CuO₄, where the ionic radii and electronegativies of Ga³⁺ and Fe³⁺ are similar. The dielectric properties of InM³⁺Cu[subscript 1-x]Mg[subscript x]O₄ (M³⁺ = Al and Ga) were found to be the result of the Cu²⁺ d⁹ polarizability, but there were extremely large loss values because of remnant semiconductivity. All compositions were found to be frustrated antiferromagnets with spin glass behaviors at low temperatures, but when more than one magnetic cation was present, the magnetic properties showed indication of slight ferrimagnetism between the Fe³⁺ and Cu²⁺. The solid solutions of InGaMMꞌO₄ (M = Mg, Zn; Mꞌ = Co, Mg) displayed similar structural results to those found in the previous solid solutions, although the differences in electronegativies were not as influential. The optical properties of the cobalt containing compositions verified that the M²⁺ cations were located in a disordered trigonal bipyramidal site, with a dark purple color resulting from prominent d-d electronic transitions. The magnetic properties of the InGaMg[subscript 1-x]Co[subscript x]O₄ solid solution indicated that these compositions were spin glass systems with short-range antiferromagnetic interactions. To compare the trigonal bipyramidal layering schemes, the In₂Fe[subscript 2-x]Ga[subscript x]CuO₇ solid solution was compared to that of InFe[subscript 1-x]Ga[subscript x]CuO₄. The structural parameters of In₂Fe[subscript 2-x]Ga[subscript x]CuO₇ mirrored those of InFe[subscript 1-x]Ga[subscript x]CuO₄, but the magnetic properties were found to much more complex with the additional trigonal bipyramidal layer. It was determined that the single trigonal bipyramidal layer ferromagnetically interacted with the antiferromagnetic interactions within the double trigonal bipyramidal layer, particularly with x ≈ 1.