Reconstructing subdivisions and making an object lower resolution

Draw a sphere3D

Convert to Polymesh:

The Geometry submenu automatically changes:

  
Hit Reconstruct Subdiv followed by Del Higher ...
Do this sequence several times ...

 

  

 

If you instead loaded the tool PolySphere ...

You will see it has a lot more polys ...

You would have to remove the higher ones first.

Hit Lower Res, then Del Higher repeatedly

  

... until the option to decrease any more is unavailable.

This is the appearance to the tool redrawn:

Then you would proceed the same way as above, by reconstructing subdivions. Note the Polysphere does not have poles like Sphere3D.