I could use some help with a math problem, for a computer game I'm playing, Space Engineers.

The game uses a Cartesian coordinate system, with XYZ coordinates. I have a planet with known coordinates for the center, and the coordinates for a space station. I want to place objects at five other points, like the corners of a cube. I'd guess it was a simple math problem to get the point on the opposite side of the planet from the space station, but I don't know how to work out the other four points.