So, lately I've been doing some physics thinking about Crux, inspired by the scene in Six Sided Fate where they walk from one face of Crux to another. It made me wonder: what would it actually be like if you crossed from one face of a cubic planet to another?
While I cannot answer for the actual feeling during the process, I realised something that might seem paradox. If you jump diagonally (equal increase of height and length of jump), gravity will pull you back to the edge (while I read that a cube's gravity does not exactly point to its centre, it roughly does), so you will fail in passing to the other side, I think. So, how should one jump in order to successfully pass to the other face? After some thought, I conclude that a high jump will more easily (if not exclusively) transfer one to the other face. Seems odd, doesn't it? The gravitational force pointing roughly to the centre of Crux can be analysed in a horizontal and a vertical force (perspective of the current face). If one jumps high (and slightly forward, otherwise you'd get back to the same place), the horizontal force pulling you back is weaker than the vertical force pulling you down. Well, actually, I could be wrong. The longer distance in height means there is a bigger distance to cover before one is sufficiently pulled back so that their fall may be stopped by the ground. To be sure whether it is easier (indeed if it is possible at all), I would need to study the subject more closely in all its glory of math and physics.
However, these thoughts brought me another idea, as they may have done with you, if you understand physics well. The analysation of gravity to a horizontal and a vertical force means there's one force keeping you to the ground (vertical) and one pulling you towards the centre of the face on which you are on (horizontal). Now, at first I supposed it wouldn't be a very significant force. Turns out I was wrong.
Yesterday, I googled 'cubic planet physics' to see if other people had answered the questions of how a cubic planet would be like and see if I was right. I was glad to find there were indeed other people wondering about these stuff. Firstly, it should be noted that an Earth-sized cubic planet cannot exist in reality, because its gravity would cause it to assume a sphere-like shape, like mountains cannot be too tall on Earth. Then, the physicist went on to confirm my theory that one would be pulled towards the centre of the face of a theoretical cubic planet they were on. However, the horizontal force is much greater than I thought. The writer said that the face would feel like a bowl and if you tried to walk around the planet's equator it would not be like walking on constant altitude of zero, but instead the phenomenal altitude would get many times bigger than that of Mount Everest and it'd be even worse at the corners.
While that is very amazing, there is more. This pull towards the centre means that all air and water would concentrate in a small area around the centre of the face. Hence, the majority of the planet would be a barren wasteland with no atmosphere. Meanwhile, there would be six independent bubbles of water and air, the only places where life could exist.
My source, for further details and pictures:
What would Earth be like to us if it were a cube instead of spherical ...