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 (current)
Section 10: Placement of the South Pole Corners
Section 11: Orientation of the Southern Equatorial and South Pole Corners

9. Placing the southern equatorial corners

Now we really have a little problem: Whereas the edges are all set, there are still two kinds of corners to be set: the southern equatorial corners and the South Pole corners!

Of course, we do not want to disturb the order of the edges any more! Hence, we must find operations for "working" on the corners which leave "undisturbed" the edges.

Luckily our elementary operations provide us with just this property. In order to fully understand this, let's take a very close look at our elementary operations again:

All of our operations: L**, R**, R**, L** exchange two pairs of corners. Hence, after repeating any of these operations two times, these respective corners are back at their original places. But these operations also move around three edges: Hence, by repeating any of these operations three times, the edges will have been moved back to their original places, whereas an exchange of the corners remains.

This is the simple idea for our next procedure: In order to set our corners, we shall always apply any of our elementary operations three times. In this way, the already established order of the edges will not he disturbed


Now, let's get started. There may be some southern equatorial corner already correctly set. That's just too fine. If you find a southern equatorial corner correctly placed but wrongly oriented, do nothing with this one for the moment. We shall worry about orientation later. For the moment, we just want to place!

If you find a southern equatorial corner not properly placed, turn MEGAMINX to bring this corner in front. Now look where the appropriate corner is which really belongs to this front place. We have to distinguish two cases

Case 1. The southern equatorial corner belonging to the front place is in the South Pole cap. Bring this corner in front by turning the South Pole cap. "Send" it down to its place by applying {R**}3.
Bring the corner to
be placed in front



{R**}3

Again, for the moment, we don't worry about orientation.



Case 2. The southern equatorial corner belonging to the front place is somewhere in the equatorial belt.



By turning MEGAMINX, bring this corner in front and apply {R**}3. This operation "lifts" this corner into the South Pole cap. Turning back MEGAMINX, you are in Case 1 again.


In this way, you place all the southern equatorial corners. Finally, turn the South Pole cap so that all edges are set correctly again.

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