:-D Easy peasy, lemon squeezey.
;-) First, create the primitive: a sphere with eight layers and sixteen squares in each layer. Be sure the "stagger points" option is unchecked. This way, we have ready-made squares, ready for coloring.
Since the default color of a primitive is white, we need only to color every other square red. We'll do this by selecting the squares we wish to color and defining them as a subgroup. Then we can use the attributes requestor on them to alter different characteristics, including color.
;-) To select the squares we want, we'll use the "hide points" function to hide the lower half of the sphere first, so that we are selecting faces only in the top half. Next, set the "pick mode" to "pick faces," and the "pick method" to "lasso" or "drag box." select the two faces which comprise one of the squares. Then hold the shift key down while selecting another. Work your way around systematicaly until you've selected all of the red squares, but none of the white ones.
Now select "make subgroup" from the "functions" menu. Give the subgroup a name such as "scarlet" or "crimson."
Now use the "attributes" requester to define the color.
Next, set the selection mode to "pick objects" and refresh the screen, so that the lower half is re-drawn.
;-) Repeat as above, hiding the upper half and working on the lower half this time. Be carefull not to choose the wrong squares to color red. Otherwise, your Boing Ball will look funny at its equator. Give this subgroup a different name, so as not to overwrite the first subgroup.
Now quickrender the object to insure the colors are lined up correctly at the middle. re-define one of your subgroups if you've goofed it up.
:-D Finally, save your new toy.