# Finding Symmetries of Points on a Sphere

Currently, I am working on a project where I would like to find symmetries of points plotted on a sphere. One example would be to rotate the sphere 180 degrees about the x-axis and the picture would look the same. I am looking through many different formations of points and am wondering whether or not there is a way to speed it up and to increase the accuracy. Is there a function to find rotational symmetries about different axes (as they are not limited to x,y, and z)? If relevant, my points are currently in cartesian form, but I also have them available as spherical coordinates. Thanks!

-Chase

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You can help us help you by providing a sample set of points and the code you use for visualization, and any attempts that you have made to solve this so far. – Pickett Jul 25 '14 at 7:49
@Pickett I use ListPointPlot3D for the points and Graphics3D for the sphere. A sample set of points would be {(1,0,0),(-1,0,0),(0,0,1)}. This set has 180 degree symmetry about the z-axis. – Chase Yetter Jul 26 '14 at 0:42
You're talking about speed issues and issues with accuracy; show us the sample sets where you had these problems and what it was that was too slow. That's what I was looking for. – Pickett Jul 26 '14 at 1:18
@Pickett Some of my sets have up to 500 points. So far, I have been finding the symmetries visually, which can be very slow and inaccurate with that many points. What I meant by speeding it up is that it takes too long to look for these symmetries and that it isn't as accurate as a program could be. I don't yet have any code to find symmetries. – Chase Yetter Jul 26 '14 at 17:04