Do Four Points Define a Hyperplane or Extend Beyond?

[redretro]

If three points make a plane? what does four make 1 also until you reach 6 how does that system work?

 

[chroot]

Four points would define a hyperplane (literally, a 4-dimensional plane), but do not necessarily define a normal 3-dimensional plane -- they may not be coplanar.

In the same way, three points define a normal 3-dimensional plane, but do not necessarily define a line -- they may not be collinear.

- Warren