Where is the Polysphere object in Blender 2.76b? I have already installed Add Mesh: Extra Objects add-on and can see new objects in add menu, but Polysphere is not there. I also tried following it on the official page, but they say that the script is already part of Blender and is not needed to be installed from file. Clicking on the Current version download link opens a forum instead of the script.
I don't know if the codes comes from the "original" polysphere script, but with Extra Object add-on comes an operator called "Round Cube" which create a very similar geometry.
You'll just have to make sure to use the "Quadsphere" preset:
You can get the "original" polysphere script for pre-2.61 Blender version from the author website and then append the object in your scene (if you want to use a more recent version).
It seems to be slightly difference between the loopcuts position of the object created with the two methods.
Poly-sphere is something special. The symmetry loops on the poly-sphere should form a perfect polygonal circle made of edges with equal length.
Rounded cube or any sub-divided cube with a spherify modifier or manipulated to be spherical only give you an incorrect version of the poly-sphere.
Example, create a cylinder with 16 edges. Create a perfect poly-sphere with same diameter and segments on the perimeter. Cut the poly-sphere in half and remove the caps on the cylinder. Match the half sphere onto the cylinder's open cap, and try remove-double with threshold distance of 0 or barely 0. If what you created is truly a poly-sphere, it should merge perfectly with the uncapped cylinder.
Blender by default does not give you the perfect and real poly-sphere. It should be possible to create perfect poly-spheres by codes.