This is a Lincoln Log that is 100% compatible with the store bought items. I included files for 2 different sizes, although anything is possible.

Printing with 10% infill results in something I could break if I really wanted to, but is plenty strong enough for all practical building purposes.

I printed mine with a raft because curved bottoms seem to flatten out if I don't, and it doesn't have much of a base to adhere to the build platform.