I designed this extremely simple bracket for securing carpet material to an Ikea Kallax shelf for a cat tower I am building.

These brackets keep the carpet in place with a rubber band keeping tension between them. This allows for easy removal of the carpet for cleaning, and also if you decide to use the shelf for something else in the future.

One bracket has a lip for carpet material as the carpets I used are too wide for the Kallax. If your carpet/rug is the right width, just use 2 of the standard brackets.

I included the STEP files as well for easier modification/improvement.