Model originally uploaded to Thingiverse at https://www.thingiverse.com/thing:3626156.

I used the Twisted_Heart.stl from Athruz - https://www.thingiverse.com/thing:2781414/ (thanks for including the solid model). I wanted to make a twisting heart box using vase mode (I use Cura, so "spiralize outer contour" to be more exact). I adjusted the twist rate, size, and height in TINKERCAD. The clearance between the base and lid are based on a 0.4mm nozzle, if you are using a different size it will need to be edited. I made the base taller than the lid so that there is always some of the base sticking out. In my first version they were the same height and it was almost impossible to open if you closed it all the way.