2.1 Correct position and orientation of all corners of the cube

The goal of this step is to place all corners on the cube in correct positions and with correct orientation. In this step we do not concern ourselves with edges, because placement and orientation of edges will be a part of Chapter 2.2.

One can use several mehods for the placement and orientation of corners, which can be further combined, but in principle they may be divided into those groups:

1. Placing the corners of the upper layer with correct orientation into proper positions, then placing the corners of the lower layer, without regard to their orientation, into proper positions, followed by correctly orienting the lower-layer corners.
2. Placing the corners of the upper layer with correct orientation into proper positions, then orienting the corners of the lower layer, such that the stickers of the corners having the color of the lower side's center are pointing downward, followed by placement of corners of the lower layer such that the orientation of the lower stickers of those corners remains unchanged.
3. Placing the corners of the upper layer with correct orientation (stickers with the color of the upper center are pointing upward) into arbitrary positions in the upper layer, then orienting the corners of the lower layer as in item 2, followed by orienting the corners of both lower and upper layer simultaneously, so that the correct orientaton is preserved (as in item 2).

Sometimes the first two methods are combined with placement of the upper-layer edges into correct positions (except for one edge - gap, see chapter about solving the edges). Algorithms for the last method usually do not leave edges in correct positions,

The last method is probably the most impressive, but it is more complex, because it requires somewhat more basic algorithms, than the first two.

I assume, that you are able to place the corners of the upper layer in their positions without my help. I not, then try harder (usually it is not so easy the first time around), so keep trying or have a look at another chapters. At this stage, the cube should look approximately like this:
(stickers of arbitrary color are shown as gray)

Because any cube has "only" eight corners, and four of those are correctly placed in the upper layer, the four remaining corners are in the lower layer. We must properly position and orient those corners.

Now we will turn the cube upside down. By doing so, the lower layer becomes the upper layer, which we are going to treat.

2.1.1 Solving by the first method

Now we may have those cases:

2.1.1.1 Interchanging corners

The following table shows schemes (looking from above) of how individual corners transfer under the application of pertinent algorithms. Those algorithms leave edges in both the lower and middle layer unchanged, therefore those layers may already be completed.

L U' R' U L' U' R U2	L U2 L' R' U L U' R U2 L' U

Initially it is sufficient to master only the first algorithm. Should the second case occur, we just apply the first algoritm to arbitrary two corners of the upper layer. By doing so we obtain the first case.

If we have the corners in correct positions (without regard to their orientations), we proceed to the next step (if it is necessary - see the above table).

2.1.1.2 Orienting corners

At this stage you should have corners of the upper layer in their positions, but some should be wrongly oriented. If they are correctly oriented, then proceed to solve the edges.

The following algorithms are used for orienting corners:

R U R' U R U2 R' U2	L' U' L U' L' U2 L U2	R U R' U R U' R' U R U2 R'	R U2 R2 U' R2 U' R2 U2 R	Execution of 1. algorithm transforms to the situation in 2. picture	Execution of 1. algorithm transforms to the situation in 2. picture	Execution of 1. algorithm transforms to the situation in 2. picture

It is worth noting that the second algorithm is only the mirror reversal of the first. Instead you can use the first algorithm backwards (you must also turn the cube). The advantage is that you need not use your left hand.

Initially it is sufficient to learn the first two algorithms (just the first one, really). All the other situations are transformed to the first two after applying the first algorithm to those situations. (The cube must be oriented according to previous schemes.)

Beware! Those algorithms are not optimal, if we don't need to preserve the lower layer (they preserve the middle layer and furthermore don't change the position, only orienration, of the upper layer's corners!) It is useful to learn them, if you want to be able to solve the cube by other methods, such as the layer-by-layer method. I will state the optimal algorithms when I describe the third method.

Now you should have correctly positioned and criented corners and can proceed to solving the edges.

2.1.2 Solving by the second method

Unlike the previous method, we are not concerned with positioning the corners first, but with orienting them such that their stickers with the color of the up center cubie point upward. We wil be aided here by algorithms from previous chapter 2.1.1.2 "Orienting corners" or by better algorithms from the next chapter (2.1.3).

Now it is necessasry to move the corners into their correct positions without disturbing their orientation (the stickers with the color of the up center cubie must always point upward). For this we are going to use the following two algorithms. There can be no more cases (except correctly positioned corners). If your placement of corners is different, turn the upper layer so that the situation is satisfactory.

U R2 U' F2 U B2 U' F2 U B2 R2	U F R' F' L F R F' L2 B' R B L B' R' B

Those algorithms are not the prettiest, but then again they don't change either the lower or middle layer. If you want shorter algorithms, then look up the solution by the third method.

Now you should have corners properly positioned and oriented by this method, so you can proceed to solve the edges, but if you want to be more proficient, you should master the algorithms in the next chapter.

2.1.3 Solving by the third method

This method is greatly optimizd for speed and number of moves, but, as is ofren the case, the ability and expertise of the cuber is crucial. Algorithms of this method are all found, with the aid of the computer, to be the shortest. Of course, I do not a absolutely guarrantee this, since I developed the program :-). The majority of these algorithms do not try to preserve any edges. If an algorithm preserves edges in the lower layer, it will be labelled by a star (*). An algorithm which also preserves edges in the middle layer will be labelled by two stars (**). If an algorithm does not even preserve plcement of corners in the lower layer, it will be labelled by an exclamation mark (!).

The first step of this method differs from the previous ones. The goal is to place the upper-layer corners in the upper layer such that the color of rhe upper center cubie is the same as the color of the corners' stickers in the upper layer. You are just going to execute the same step as in the previous methods, but you will not worry about the positions of the corners, just their orientations. After this step we again turn the cube upside down.

Now we have o again orient the corners of the upper (formerly lower) layer such that the color of the center cubie is identical to the colors of the stickrs of the surrounding corners. To accomplish this, we can either use the algorithms already mentioned in the previous chapters, or use the following:

R' U F2 R2 U F' !	R F' R2 U2 F' R !	F2 U2 F U2 F2 *	F' R U2 F' R2 U R !	F R' F' U' R' U R	R' U' F' U F R **	F' U' F U R U R' *

This table exhausts all possibilities, that can occur, or that we can get into by turning the upper and lower layer, applying the algorithm, and turning them back into original position.

Now we should have reached the situation, in which corners of the upper and lower layer are correctly oriented, but need not yet be in correct positions. Correct placement may be achieved by using the following algorithms. We are looking from above at one of the sides - either upper or lower. Red arrows designate transfer of cubies on the layer as seen from above, and blue arrows designate transfer of cubies on opposite layer (as if the cube was transparent.

R U' R U R2 F2 R F R' F2	R' F R U F2 U R' F' R U' F2	R2 U F2 U2 R2 U R2	F2 R2 F2	R' F U' R2 U F' R

Now we should have corner cubies in correct position and with correct orientation. As you will surely notice, these algorithms (particularly some) are quite short and use up to three layers for rotating, so that they can be manipulated rather q quickly (of course it takes a lot of practice). Now we can proceed to placement of edges.

2.2 Correct position and orientation of all edges of the cube.

Now the situation on the cube shoud look something like this:

Next we will try to solve two arbitrarily opposite layers. We will solve the layer between those two as last. We will introduce a new concept called gap. It is a spot in one of the opposite layers to be solved, where some edge is found (which may, or may not, belong there) and which we will use for transfers of edges into those two layers.This is also the reason for not needlessly solving the upper side in solving the upper layer via the first two methods. In solving the two opposite layers we are not concerned about their relationships to the centers of the middle layer. We just turn those two layers any way we please.

We can probably use these basic steps:

1. One layer is solved (except for the gap) and therefore we solve compoletely the second layer with the aid of the gap, and finally fill the gap.
2. No layer has at least 3 edges solved. Then we will solve one side by using arbitrary gap in the second side except for one edge. We will use this place as gap for solving the entire second layer. Finally we fill the gap.
3. We fill the gaps in both layers simultaneously (depending on need). We are careful not to use an edge that is properly posiioned as a gap. Finally we obtain 2 gaps, each in a different layer. First we fill one gap by using the other, and then we fill the remaining gap.

First we solve the edges except for the last one (that is our gap). We don't need any special algorithns for this purpose. All are three-moves maximum. Look at the following examples and try to understand them. That is the simplest way of mastering this step. We will save the gap until ll edges of the two layers we are solving are in correct positions and are correctly oriented (except for the gap). In the pictures the upper corners don't need to be colored, because their position no longer matters. Only the placement of the gap matters, which is recorded in a dark color.

We label one additional mmove - C, its opposite, C' and a twofold move C2. This move labels a rotation of the middle layer. It is always a layer between two layers we eventually solve. C means rotating the middle layer clockwise looking from above. C' and C2 are similar to the already known moves.

F' C F	F C2 F'	F C F'
F C' F2 C F	F' C' F2 C2 F'

The last two algrithms are combinations - one places the edge in the middle layer and the other properly positions it.

By repeating these algorithms, and constantly rotating the upper and lower layer into posiions, that suit these algorithms, we should find ourselves in a situation, where we only need to fill the gap with the proper edge in order to complete the two layers. See picture.

Possible cases are in the following table.

F C' F' C F C F'	F C' F2 C' F	F C' F' C' F' C' F

Now we we will line up two solved layers and centers. The cube is oriented so that the unsolved middle layer is sandwiched between the solved layers on the right and left side. The cube should look approximately like this:

For this part there are several easy-to-remember algorithms. Because we have the unsolved middle layer turned toward us, it is inpractical to label the moves as C, C' and C2; therefore, we will define the following labelling for this move: "^" labels the rotarion of the middle layer upward (up-front edge away from us) and "v" labels the opposite move. We will similarly label the twofold move as "^^".

First ere will try to place the edges into correct positions without regard to their orientation. The pictures show positions, which, after the application of a given algorithm, lead to solving the cube. These edges can be arbitrarily reversed, since we will treat edge reversal later.

^ U2 v U2	^^ U2 ^^ U2	^ F2 B2 v F2 B2

Again, initially it is sufficient to learn the first algorithm only. It can be used to transfer any case to the first situation, and solve the cube by further application of it.

For edge reversal the following algorithms are helpful:

^ U ^ U ^ U2 v U v U v U2	F2 ^ U ^ U ^ U2 v U v U v U2 F2	F' L' F ^ U ^ U ^ U ^ U F' L F

In the beginning it is again possible to master the first algorithm (the second one is just a small variation of the first). By repeated use we can solve an arbitrary situation.

Unless something unforeseen happened, your cube should now be solved.

2.3 Conclusion

Solving the cube with this method (these methods) is not too common. However, it has a number of advantages. For example, very few algorithms are needed for basic solution of the cube. It can be incredibly improved and accelerated. This method is used by some very good cubers (the world champion Minh Thai is one). The disadvantage of this method is in ths use of too many so-called slice moves, or moves of the middle layer. On a new or badly lubricated cube these moves take twice as much time as the other moves. It follows that a speed of solution is greatly enhanced by a good quality of the cube.

With application of a few basic algorithms, this method takes a very short time to learn. It is an excellent method for the beginner.

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