0If the earth were a cube, with the same mass as the more traditional ball-shaped version (which is 12,756 km or 7,926 mm in diameter), it would have twelve edges that were just over 9,300 km (5,800 mi) long. In a traditional universe, this can’t happen, but for the sake of this thought experiment, let's go with it.
Let the weirdness begin (part one)
Although the six faces are flat, you can only stand upright at their centres.
As you walk towards an edge or corner, you will feel like you are walking uphill. The further you go from the centre, the steeper it will feel, even though looking back over your shoulder, the ground appears flat but feels like it is tilted.
It is because gravity pulls towards the centre of mass, in this case, the centre of the cube. In the middle of one of the faces, your head, your feet and the cube centre, line up in the vertical position. Gravity is acting straight down. Out near the edges, the centre of the cube is at a 45-degree angle to the ground, at the corners it is about 50 degrees.
It has the same effect as trying to walk out of a vast bowl. To put the size of the container in perspective, the edges will be 2,100 km (1,300 mi) “higher” than the centre of the face, and the corners will be 3,800 km (2,300 mi) “higher”. Mount Everest, is only 10 km (6 mi) high. It is why you will need the climbing gear and a good set of non-slip shoes.
More Weirdness (part two)
You will weigh less. At the centre of a face, your weight will be about 90% of what you consider now, and at the corners, you will weigh about 60%. It is a good thing if you are walking up an invisible mountain.
Weirder Still (part three)
Let's pretend we divide all the water and atmosphere on the Earth into six equal volumes each. We then place one each of water and air our cubic planets flat sides.
The water would, due to gravitational force, pool in the centre of each face in a slightly squared circle, 4,000 km (2,4855 mi) across. Not only that, it would bulge up in the centre by about 300 km (200 mi), forming a considerable lens shape.
The atmosphere would form the same shape over the water mass, extending out about 100 km (62 mi) from the surface of the water, as it does now. Life only really exists in the lower 10 km of the atmosphere, so this would make the entire habitable land surface, a ring 10 km wide around the ocean.
It would leave most of the surface of the cube in the vacuum of space. It would look somewhat like the Moon, hence the requirement of a spacesuit to walk to the edges.
