CNC machines and 3D printers are lovely things and the amount of precision linear encoders and stepper motors have today is phenomenal.

With a few simplifying assumptions, a simple experiment, the things listed in the title, and a nice little Java Gcode generator I wrote, I created the quarter pyramids shown below.

To give you a sense of scale, each layer of both pyramids is only 0.41 mm tall. The bigger pyramid is spaced at 0.8 mm and the smaller pyramid at 0.41 mm and weren't built using an actual 3D printer. They both have a full height of about 18 mm.