This talk introduces the concept of switch preservation from geometric intuition. The 2-stage interconnection network is conceivably the most compact design for switch upscaling. Switches constructed by recursive 2-stage networks typically can be controlled in the self-routing manner because the route from an input to an output is unique. Different I/O orderings make different versions of the 2-stage interconnection network. The 2X and X2 versions are known to preserve various types of conditionally nonblocking switches, which apply to load balancing, crosstalk-free optical switching, mesh connection, etc. These switch preservation theorems have been inspired by geometric shapes, including torus and Klein Bottle. Every such theorem not only allows recursive construction of indefinitely large switches but also provides deep insight as well as generality and flexibility in switch construction.