Rubik's Revenge and beyond

Understanding the Origin of Parity Errors and Solving by Logic

4. Case 4: OLL Parity Error (misorientation of two edges)

Wondering how to resolve this parity error?

Once you understand how to create it, reversing the error becomes relatively straightforward. The key tip in this guide is to begin by commuting three edges, aligning the parity error within the same inner layer and thereby producing the PLL error of case 3.

For the sake of variety and to introduce a new scenario, let's consider the previous result and apply the commutator indicated by the green arrows in Figure 4.10. To observe a detailed demonstration of this commutation, please click play (▷) on Figure 4.11.

Following that, similarly to case 2, perform a commutation on three edges within the layer where the error is located. The objective is to ensure that the faces of the problematic edges display the same color on the same face. In our example, we can choose edges with the red color on the blue face or edges with the orange color on the blue face; either option works. For the sake of continuity, let's select both orange edges on the blue face.

To enhance visibility, let's exclude the R layer from our drawing in Figure 4.12. This allows us to better observe the commutator indicated by the green arrows. Once this commutation is executed, simply rotate the Rm layer to correctly position the edge colors. For a detailed depiction of the edge commutation and the resulting alignment, please click play (▷) on Figure 4.13.

Ultimately, only the centers of the four faces remain to be commuted. This can be accomplished using the same approach demonstrated earlier, solving one face at a time, or by employing slightly more intricate commutators and conjugates.

For a slight variation, instead of solving each face individually with three commutators, we will utilize two commutators to address two faces simultaneously. This method provides a little diversity in the solving process. To explore the specifics, please refer to Figure 4.14, and click play (▷) to observe the detailed demonstration.

It is important to highlight that, similar to case 1, the occurrence of this OLL parity error (or PLL in case 3) is limited to edges that have their corresponding equidistant pair on the side of the cube. In other words, this error never manifests with the central edges of an odd-sized cube, such as 3x3x3, 5x5x5, 7x7x7, and so on. To visualize some examples of OLL parity errors in larger cubes than 4x4x4, please refer to Figure 4.15 below.

Additionally, it is crucial to understand that OLL errors in larger cubes, such as 6x6x6 or 7x7x7 as depicted in Figure 4.15, may not necessarily be confined to a single side. These OLL variations can manifest in different configurations across the cube. To explore specific examples of these OLL variations on the 6x6x6 cube, please refer to Figure 4.16 and click play (▷) to observe the animation.

Similarly, the corresponding "companion" parity error of this OLL error, namely the PLL of case 3, does not necessarily require the edges to be swapped within the same layer. Permutations can lead to this error occurring in different layers or sides of the cube. To explore examples of these variations, please refer to Figure 4.17 and click play (▷) to observe the animation.

In conclusion, it can be observed that both the PLL error in case 3 and the OLL error in case 4 are essentially the same error, differing only in the final permutation of edges. When this final permutation involves edges with identical colors, the error manifests on the same side, leading to the illusion of a misorientation (flip) of the pieces. Hence, it is referred to as OLL, as it creates the deceptive impression of a mere misalignment of the pieces.

App source: animcubejs.cubing.net/animcubejs.html