I disagree. How often do you transport a cubical box through another one the same size while moving furniture? (It might feel intuitively clear, like flatness of the Earth or the fact that heavier objects fall faster than lighter ones…)
The equivalent question is, is there a projection of the cube along some axis so that the shadow contains a square that does not touch the edge of the shadow. That is not obvious. It isn’t tremendously difficult to show using Cartesian coordinates, but keep in mind these were invented during Rupert’s lifetime; while his big sister Elizabeth, Princess of Bohemia was a penpal of Descartes, I don’t know how fluent Rupert was in the technology.
