I'm trying to parameterize a sphere so it has **6 faces of equal area**, like this:

![correct parameterization](https://i.stack.imgur.com/jD1uF.png)

But this is the closest I can get (simply jumping $\frac{\pi}{2}$ in $\phi$ azimuth angle for each "slice").

![closest i can get](https://i.stack.imgur.com/u66HY.png)

I can't seem to get the $\theta$ elevation parameter correct. Help!