In this work, we present a method to obtain positive-genus space-filling shapes. An important property of these these space filling shapes is that they do not form links and knots. They, therefore, can potentially be assembled and disassembled to construct larger shapes. Our methodology is simply to use close curves that do not forms links and that are closed under symmetry operations as Voronoi sites. Another property of these shapes, they can be combined to create higher genus surfaces. The new combined shapes can also fill the space without having any voids between them. From our preliminary structural evaluations, we posit that higher genus tiles may allow for better inter-locking behavior as well. Therefore, many further studies need to be done to characterize and categorize this class of Voronoi sites that could produce different types of higher-genus tiles and the corresponding mechanical behaviors.