So we want to build a sphere and its nice square uvmapping.
First, in the 3d view, lets fly above the XY plane with 7 key.
We add a UV default sphere, using SPACEBAR -> ADD -> MESH ->UV SPHERE,
keeping the segments and rings to their default values ( 32 )

Then we select both pole vertices and without any mercy, we delete them:

Select both the resulting pole rings, ALT-RMB helps here:
( ALT-Right Mouse Button )

Switch to side view with 1 or 3 key.
Hit E key to extrude the two rings, and scale these along Z axis with S key and MMB (middle mouse button )
(time to let that odd wheel mouse in a cardboard and get a real
blender-victim 3 buttons mouse; if you still are
the happy owner of a working 2 buttons mouse, use S key then Z key to force Z-only sizing)

Now hit A key to deselect the rings, and with ALT-RMB, select the top ring.
S key to scale it down to almost a point - not too much, I noticied,not sure why, it makes the baked texture odd -

Now lets place the ring to its real sphere-pole location, ie just on
the grid line above the sphere ( G key+ MMB or G then Z - will you find
a decent 3 buttons mouse ? )

Repeat the steps for the bottom pole:

Ok, we have our sphere built with the good vertices topology.
Here I take a pause to say that on the main tutorial page, I made all
the faces triangular to match better the SL prim faces as described here.
This can be achieved by using a decimate modifier with a 1 RATIO.
Select the sphere in OBJECT MODE, add a Decimate modifier, hit
apply, you're done.
For the following of this tutorial, we will go on with the shpere with square faces, but the process is the same.
Now we want to project our sphere to a perferctly filled square UV-map.
First, select UV Face Select Mode in the 3D view, and in the UV image
editor, create a 64*64 image with IMAGE -> NEW menu button,
giving the right numbers into their respective fields .


Hit A to select all faces, then U to enter UV projection menu, here you choose SPHERE FROM VIEW
( I assume you still are in side view, 1 or 3 key if you messed with views):

UV/Image editor should turn into this:

I don't know why, blender has the odd idea to project four quads outside the UV image space, but we will show him !
(maybe a smartly placed seam would help ? )
In the 3d view, still in UV Face Select Mode, hit A key to deselect all
faces, then select the faces with odd projection (RMB, shift RMB)
, here you only have to find which is which, good luck :)
At least it is around the top pole:

In the UV MAP editor, the four bad quads are now alone in evidence:

move these to the top left corner ( G, CTRL-MMB, or G, then X then CTRL-LMB ) :

We have been strong, its almost finished, just hit A key in the 3d view to select all faces,
you should have your very nice and aligned square spherical UV projection ^_^ :

Thats it !
What we saw, is that blender's spherical UV projection is odd, that its
worth saving our file at this point, to reuse it later without having
to redo all these steps, that the best idea is to reuse the sphere from
the template instead of spending 20 boring minutes to recreate
it, and that we want to find a store that still sells 3 buttons
mouses.
Click here to return to the main tutorial page ^_^