Megaminx
Solution
by Kurt Endl.

Fast Forward to:
Section 1: The Objectives
Section 2: The Elementary Operations
Section 3: Construction of the North Pole Cap
Section 4: Setting the Northern Equatorial Edges
Section 5: Setting the Northern Equatorial Corners
Section 6: Setting the Middle Equatorial Edges
Section 7: Setting the Southern Equatorial Edges
Section 8: Setting the South Pole Edges
Section 9: Placing the Southern Equatorial Corners
Section 10: Placement of the South Pole Corners (current)
Section 11: Orientation of the Southern Equatorial and South Pole Corners

10. Placement Of the South Pole corners

Now we get to one of the roost tricky parts of our game. We must place all South Pole corners, without destroying anything else!

This is not possible without "breaking into" the equatorial belt again. But, take it easy! At the end of our operations, the equatorial belt will be restored!

We shall use the operations (L**)³ and (R**)³. As you know, these operations also move two northern equatorial corners. Hence we want to be careful to keep the lower part of MEGAMINX fixed such that only two such corners exchange continually: Choose any standard position of MEGAMINX and stick to it.

If there is a South Pole corner wrongly placed, bring it in front by turning the South Pole cap. Apply {R**}³ to "park". this corner in the equatorial belt, and turn back the South Pole cap in order to set correctly all edges again.

Now, look for the place in the South Pole cap to which the "parked" corner belongs. Bring this place in front by turning the South Pole cap. Then "lift" the "parked" corner to the South Pole cap again by applying {R**}³ . Finally, turn back the South Pole cap in order to set correctly all edges again.

In this way, you will place correctly all South Pole corners. When these corners are all set you will see that also the two northern equatorial corners, which exchanged continually, will be back at their places.