I've got a noisy set of points that lie on/near a unit 6-sphere. I want to visualise their proximity to the sphere in some way. The only way I can come up with now is a histogram of the norm of the points (See below). For 2D and 3D this is simple, but is there a way to do this for higher dimensions other than a histogram?
In other words, is there a way to project 6 cartesian coordinates $x = (x_1,x_2,x_3,x_4,x_5,x_6)$ with length 1 onto a unit circle/3-sphere?
