Given X is the spatial dimension of a plane/hyperplane, What's the best way to calculate if any set of points in N dimensions lie in the same 1D plane (collinear) / 2D plane (coplanar) / 3D plane (cocubic) / 4D plane (cotessar) / XD plane (co-X-spatial) etc.
I have tried using the rank of matrices of points as noticed here asper
specifically what I did was e.g. if the rank is $<=$ 3 then the points are cocubic just like if the rank is $<=$ 2 for being coplanar, sadly that didn't work. Then I saw this which is why I am asking about the best way to actually get this done.
cubic and tessar from cubes and tesseracts