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The multiferroic systems RAl₃(BO₃)₄ (R=Ho) is known to exhibit significant electric polarization. However, the more general class containing Fe at the Al site shows only weak polarization. In this work we conduct detailed structural measurements of the full class of RA₃(BO₃)₄ (R=Sm, Nd, Ho, Gd, Eu, A=Fe, Al). Temperature-dependent single crystal measurements between 15 and 300 K are used to track the structure to enable modeling of the electronic properties. Direct comparisons between the RAl₃(BO₃)₄ and RFe₃(BO₃)₄ are made.