A- Mosaic Sphere

- The Objective -

So the usual sphere in 3D apps will make X sides incident in the pole and Y segments that are evenly distant. (How is this type of sphere called/designated?). Near the poles this sphere quads look very rectangular and some times that is not good.

So, what i would like to get is this type sphere, but where the quads are the most squarish/regular as possible. For this the parallels/segments distance will have to different, being smaller in the poles.

-Attempts-

Here's a comparison between the usual sphere and an eye balled Mosaic Sphere to explain the objective.

I also tryed to do the following using an expression like x^3, took the y values in a straigth line, Bend it 90º and the made a Lathe, to make a semi-sphere. It's not great, but looks just ok, because i think x^3 or something like this is not the right expression.

So i started to think which shape would be more close to a square between 2 angled guidelines. And it seems to me that a 3-sides equal trapezium might be it.

So what function/expression would give me the heights of such polygons? If i could use such, i would just need to bend the Y values and make a Lathe to have this thing done properly.

Cheers