2024-04-01 UPDATE: I just bought the Q-Tip brand of swabs and they are slightly longer than the generic brand. I have updated the model file to be 2mm wider to accomodate the length of the Q-Tip branded swabs.
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I had found a dispenser that was about what I wanted, but the STL had alignment issues and I had some improvements I wanted to try, so I made this from scratch. The inner width is slightly wider than a generic Q-Tip, the front has raised sides to prevent them from spilling out, the front has angles and a rounded cutout to make it easier to take one. You should be able to fit more than an entire package in it.
I printed this in white PLA at 0.2 Standard with no supports needed.