# Plotting 3 equidistant points on a sphere

I'm trying to figure out how to plot with $x,y,z$, three points that are equidistant along the surface of a sphere from each other that are all on a horizontal axis (so $y = 0$) with a radius of $500$ with the first point being at $(0, 0, 500)$ - or, if you were looking at the sphere at eye-level, the point closest to you. I've tried looking into the Cartesian system but think I'm either not getting it or am barking up the wrong tree. Any assistance would be greatly appreciated, thanks so much!

To clarify I'm writing some code that causes a user's camera to rotate around a central focus point and plan on using these coordinates as $3$ standard camera settings to rotate to, hope that helps!

By equidistant if you mean that the shortest distance between any pair of these points is the same then there are an infinite number of correct answers. For example $(0,0,500),(0,-250\sqrt{3},-250),(0,250\sqrt{3},-250)$ lie on a great circle and are equidistant.
• And these are. The distance along the sphere between any pair is $500\frac{2\pi}{3}$ – Paul Sundheim Dec 31 '14 at 20:37