Machine / scribe 15 equidistant circles onto sphere surface

[Easibook]

Hi guys - hope you can help ! I am trying to machine 15 equidistant circles onto a plastic sphere, 5 circles in each plane (X,Y & Z.). Each circle can be simply scribed in place - but they need to be very accurate, and any error shows up when the lines do not all cross at the same point etc.

I have tried locating the sphere in between two bars (which have a CNC machined depression the same radius as the sphere in both ends)with the two bars located in a lathe. One bar then has a spring loaded spike in its centre. The first series of scribes is easy enough, one at the spheres circumference, and 2 left and right. The Sphere is then rotated through 90 degrees until the pin lines up with the centre line, and another 5 lines are scribed and repeated one last time for the last plane.

The problem is error creeps in and the lines do not intersect exactly as they should.

Is there a better way to get 15 concentric circles ( 5 in each plane) exactly equidistant from each other on a lathe ?

 

[EdDanzer]

There is a process where a laser can make 3D pictures in a block, or sphere. This may be the only way to do it in 1 setup.