Say that you have a planet that, instead of being spheroid, is cuboid. How would such a planet form? Wouldn't the gravity pull the matter toward the corners toward the center, causing the planet to revert to a sphere? (Hoping for an answer rooted more in hard science and less in reversing the polarity.)
It would not form on its own
Wouldn't the gravity pull the matter toward the corners toward the center, causing the planet to revert to a sphere?
So if you find a cubic shape in space, it would by definition not be a planet. It would also be very small, not more than the size of large asteroid / dwarf planet. And it would in all likelihood be artificially made, because the only natural formations that turn out cubic are crystals, and those are way too dense to be able to maintain their cubic shape when reaching planet size.
Leaving aside the issue of how could a cubic planet be formed, or how could it keep its cubic shape, let's understand how it feels on the ground. If physic laws as we know them apply to it, those living upon it - or merely visiting - won't feel it like a cube. They will feel it like a planet with eight monstruous mountains. Yes, you guessed right, those monstruous mountains are the vertexes of the cube. Everything will roll down those mountains to the plains in the centre of each face of the cube. This includes water and atmosphere: the oceans, if there are any, will be at the centre of each face, and their surface will not run parallel to the solid surface of the planet; it is going to be curved, and its curvature will be that of a spherical cap. The same goes for atmosphere; the atmospheric pressure in the centre of each face is going to be much higher than in the vertexes. You know that Earth's atmosphere is already irrespirable at the top of the Everest. Consider that the Everest, tall as it is, hardly makes the Earth look polygonal; what happens in a cubic planet is that either the atmosphere is inexistent at each vertex - and in a huge area around each vertex - or irrespirably dense at the centre of each face.
How tall would those monstruous mountains be? Suppose the distance from the centre of each face of the cube to its baricentre is 12,000 kilometers - so that gravity there would feel like gravity on the surface of the Earth. Now, your planet would be like a cube circunscribed to a sphere the same size of Earth. The vertexes would then be at 16/pi^2 multiplied by 12,000 kilometers from the centre. This is a little more than 1.6 times 12,000 km - or some 19,400 km. Which means, those would be mountains 19,400km - 12,000km, or 7,400km tall. Mountains about 900 times taller than the Everest.
Such things would crumble down catastrophically if your planet is governed by ordinary laws of physic. So, if you really wish a cubic planet, the region of space in which it is placed must have different laws of physics. Those will be complicated, and will need to be taylored to the specific effect you wish (if you want for each face of the cube to feel like a plane landscape, it needs given physic laws; if you want them to feel like described above, but even then to the planet somehow keep its shape, then you need a different set of physic laws).
I have no idea of what such physic laws should be, but this gives you the question that you need so that you can get the answers from the physic-enabled minds here; you need to ask what should the laws of physic be so that a cubic planet could be possible.
Well gravity works as mass attracting mass, so even if the mass of the cube was cubical, the cube would still work as if there was a sphere underneath. So standing on the center of one side, you would stand vertically, while if you were on the edges, you would be pointing towards the exact center. (so at an angle to the horizon). However, as you would be further from the center you would be pushed towards it, yes. Somewhat similar to how you are "pushed" downhill on our planet.
Unfortunately, this also means that any large shape floating in the universe would eventually become a sphere, as it is attracted to the center of itself.