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Clos networks and their folded versions, fat trees, are widely adopted in interconnection network designs for data centers and supercomputers. There are two main types of Clos networks: strictly nonblocking Clos networks and rearrangeably nonblocking Clos networks. Strictly nonblocking Clos networks can connect an idle input to an idle output without interfering with existing connections. Rearrangeably nonblocking Clos networks can connect an idle input to an idle output with rearrangements of existing connections. Traditional strictly nonblocking Clos networks have two drawbacks. One drawback is the use of crossbars with different numbers of input and output ports, whereas the currently available switches are square crossbars with the same number of input and output ports. Another drawback is that every connection goes through a fixed number of stages, increasing the length of the communication path. A drawback of traditional fat trees is that the root stage uses differently sized crossbar switches than the other stages. To solve these problems, this paper proposes an Identical Strictly NonBlocking folded Clos (ISNBC) network that uses equally sized square crossbars for all switches. Correspondingly, this paper also proposes an Identical Rearrangeably NonBlocking folded Clos (IRNBC) network. Both ISNBC and IRNBC networks can have any number of stages, can use equally sized square crossbars with no unused switch ports, and can utilize shortcut connections to reduce communication path lengths. Moreover, both ISNBC and IRNBC networks have a lower switch crosspoint cost ratio relative to a single crossbar than their corresponding traditional Clos networks. Specifically, ISNBC networks use 46.43% to 87.71% crosspoints of traditional strictly nonblocking folded Clos networks, and IRNBC networks use 53.85% to 60.00% crosspoints of traditional rearrangeably nonblocking folded Clos networks. Full article