Aborted after printing two pyramids and realising that the model does not make a cube, with different values for the x, y and z measurements.
There was also identical bubbling near the tip of both pyramids.
Ultimaker 2 Extended
I fixed the file and it does work correctly now
I ended up modelling my own pyramid based on your idea, to which I added velcro to hold the pieces as a cube. I have shown it to a few people who had that great "aha!" moment.