Is this mechanical design possible?

Hello.

For a project, I'm trying to make a fully modular toolbox system that is unique from others on the market. The main thing that makes it unique is that I want every divider in the system to be the same design with the same interlocking features at the end, so that there are no horizontal-specific or vertical-specific dividers. Also, any shape I would like to make with the dividers should theoretically be possible. If I want to connect to only 1 wall, and create a divider 4 dividers in length, like a dam with one piece perpendicular, that should be possible all with the same design. The problem I'm running into is that after hours of attempts, I can't seem to find an interlocking feature design that works. Ideally, all connections are made at the tips, and all attachments are made perpendicular or parallel to the dividers. I was hoping to 3D print the dividers, so they will have a level of thickness to them, and the features would have either male or female dovetails. I've tried things such as male connections on the 0 and 90 degree sides and female on the 180 and 270 degree sides, the 0 and 180 being male and the 90 and 270 being female, and many more, but none of them are able to work with just one design. What I'm wondering now is if my design, a modular divider system with only 1 designed divider that can theoretically always have a working solution for any shape, is even possible. If it is, any guidance for how each side of each interlocking feature should look? I'll try to answer any questions.