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The authors consider the switch-block design problem for three-dimensional FPGAs. A three-dimensional switch block M with W terminals on each face is said to be universal if every set of nets satisfying the dimension constraint (i.e. the number of nets on each face of M is at most W) is simultaneously routable through M. A class of universal switch blocks for three-dimensional FPGAs is presented. Each of the switch blocks has 15W switches and switch-block flexibility 5 (i.e. FS=5). It is proved that no switch block with less than 15W switches can be universal. The proposed switch blocks are compared with others of the topology associated with those used in the Xilinx XC4000 FPGAs. Experimental results demonstrate that the proposed universal switch blocks improve routability at the chip level. Further, the decomposition property of a universal switch block provides a key insight into its layout implementation with a smaller silicon area.