This morning I have tried to create a shell of a sphere (see the figure).
However, I would to have the entire shell where I can see to complete revolution on the other side of the sphere. What should I do?
Starting with three shapes
If you want perfectly round stripes, revolve a splitted half circle, a group which consists differently colored pieces. An example:
Here all stripes are equally wide. As well you can at first make a circle and split it arbitarily
Draw a vertical line (=hold shift as you draw)
Make a rotated copy (Object > Transform > Rotate > 15 degrees, Copy)
Draw a circle which has center at the crossing (Hold Alt+Shft as you draw, be sure that you have smart guides and snap to points ON, no other snaps!)
With the Scissors tool split the circle at the crossings, delete everything else than the 15 degrees arcs
Make rotated copies until you have a full circle (Object > Transform > Rotate > 15 degrees, Copy, repeat by pressing Ctrl+D)
NOTE: 15 degrees was selected because it's integral part of 180 degrees.
Delete the left half of the circle, color the remaining arcs and group them
Revolve the group to make a sphere
If you want different division to stripes, you can in step 2 make more marking lines with different rotation angles. After inserting the circle you split it at the crossings.