I am working on a project that requires deriving from a single 3d coordinate (x,y,z) a 3d space having a random shape of a geometrical figure e.g. a cube-like figure.

The idea is to build a 3d geometrical figure that will contain the single 3d coordinate. For example, one way is to derive from the initial (x,y,z) various other coordinates in 3d space by extending it (e.g. (x+,y-,z+) derives a new coordinate by extending the initial x,y,z).

Question is. How many coordinates are required to build up this 3d space? I am estimating that 8 should be required (x1,y1,z1),...,(x8,y8,z8). Is there a way to do this by computational means?

Thank you for your help in advance!