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'''Edge Pairing''' is the substep of [[Reduction|reduction methods]] for [[big cubes]] in which [[edges]] are paired, completing the reduction to [[3x3]] (plus possible [[Parity|parities]]).

== 3-2-3 edge pairing ==
'''3-2-3 edge pairing''' is a technique to pair the last eight dedges on 4x4x4 and up in pairs of 3, 2 and 3.

This is accomplished by placing the four already solved dedges on the bottom face (in most methods like [[Yau]] or [[Hoya]], this is already done in the [[Cross]] step). After that, a Uw (or Uw') move is performed to misalign the centers. Then, the solver solves three edges by looking at the edge on the top left of the E-slice and placing the corresponding edge in the bottom right, so that they would pair if a Uw' (or Uw) were to be performed. This is repeated three times and followed by a Uw' (or Uw) to pair up the three edges. The next two edges are solved via the "standard/beginner way", which is to place two edges in the E-slice, pair them with a wide U and insert another edge so that two edges are paired in the end. For the remaining three, this is repeated again (since it is impossible for only one dedge to be incorrectly paired on 4x4x4, the last step pairs up one more dedge than the one before it).

Although this method of edge pairing is the most popular one among 4x4x4 solvers, especially for [[Yau]], it is usually not used for 5x5x5 and big cubes.

== 4-2-3 edge pairing ==
'''4-2-3 edge pairing''' is a technique to pair the last nine dedges on 4x4x4 and up in pairs of 4, 2 and 3.

4-2-3 is done almost identically to [[3-2-3 edge pairing]], except that the first slice solves an edge. After slicing back, 3 more are solved. This is followed by another 3 edges and the final 2, thus 4-2-3. While mainly used on 4x4x4 for [[HK+]] & [[APB4]], this can also be applied to 5x5x5 by first solving the outer wings using 4-2-3, and then solving the inner ones using 4-2-3 with slices.

== 6-2 edge pairing ==
'''6-2 edge pairing''' is a technique to pair the last eight dedges on 4x4x4 and up in pairs of 6 and 2.

Like in 3-2-3 edge pairing, the four paired dedges are placed in D and the solver puts three edges relative to each other so that they would be paired by a Uw (or Uw'). However, no wide U move is performed before placing the edges. To create three dedges, the Uw (or Uw') is performed. This is followed by pairing three edges again the same way (although now, the centers are misaligned by a Uw' (or Uw)). To finish pairing the six dedges, the Uw' (or Uw) move is performed. Now to finish the last two dedges, the edge in the U layer is put diagonally from the other unsolved edge in the E-slice (e.g. one in BL and one in FR position) so that the top and bottom of both edges match (i.e. one dedge won't be paired by a Uw2). To pair both edges at the same time, the solver performs a Uw2, a flipping algorithm and another Uw2.

6-2 edge pairing is the second most common edge pairing technique among 4x4x4 solvers (after 3-2-3) and often used in conjunction with [[Hoya]] (although it can also be used with any other method that pairs up four edges beforehand, e.g. [[Yau]]). Similarly to 3-2-3, it can also be applied to 5x5x5+ but isn't really used by anyone.

==5-3 Edge pairing==
5-3 Edge Pairing is an experimental 4x4 edge pairing method.  An optimization of 6-2 edge pairing that forces a 3-cycle at the end of edge pairing instead of a 2-cycle, except for some special cases.  It ends up being more move-optimal than 6-2 on average while maintaining similar lookahead to other edge pairing methods.

== Freeslice edge pairing ==
[[File:Freeslice.png|frameless|right|100px]]

'''Freeslice edge pairing''' is a technique used on [[big cubes]] ranging from 4x4x4 and up in which the [[slice]]s between the U and D [[layer]]s do not have to be re-solved immediately after an edge pair is formed. Rather, the slices are re-solved after 8 edges (or only 4 if 4 other ones have already been created like in [[Yau]] or [[Hoya]]) are paired and when there are only 4 edges are remaining to be paired. 

Essentially all world-class big cube solvers use this technique for 5x5x5+ to some extent and it is also the most common one for puzzles higher than 4x4x4. When this is combined with the [[Reduction Method]], the result is usually referred to as the [[Freeslice Method]].

== Free-2-3 edge pairing ==
Free-2-3 edge pairing is an 4x4 edgepairing method, that essentially is a mix of [[Freeslice edge pairing]] and [[3-2-3 edge pairing]]. The first 3 dedge pairs are solved like [[Freeslice edge pairing]], and the rest like [[3-2-3 edge pairing]].

== AvG edge pairing ==
'''AvG Edge Pairing''' (named after [[Arnaud van Galen]]), also called ''
'2 edges at a time''' pairing, is an edge pairing method for the [[5x5]].
Notable users of it are [[Arnaud van Galen]], [[Erik Akkersdijk]] and [[Durben Virtucio]].

== Big Cubes edge pairing ==
'''Big Cubes edge pairing''' is an edge pairing method for the [[5x5]] and bigger cubes, popularized by [[BIGcubes.com]]. Together with [[AvG edge pairing]], it is the main edge pairing method for 5x5. For bigger cubes, Big Cubes edge pairing is by far the most popular method among top cubers.
Notable users of it are [[Dan Cohen]], [[Kevin Hays]], [[Feliks Zemdegs]], [[Mats Valk]], [[Max Park]] and [[Seung Hyuk Nahm]].

== UEF8E ==
'''UEF8E''' is a method for pairing the first eight edges on [[big cubes]]. By using U2, the solver can avoid cube rotation and using flipping algorithms like F' L F U L2 U'. While it reduces the move set (<L, Lw, 3Lw, U, R>-gen on 6x6x6 and <L, Lw, 3Lw, 4Lw, U, R>-gen on 7x7x7), the solver has to memorize four useless wings.

== See also ==
* [[BIGcubes.com]]

== External Links ==
* YouTube: [https://youtu.be/YV5AyZCrGtQ Explanation of 3-2-3 and 6-2 edge pairing]
* YouTube: [https://youtu.be/Q5O-r-r_sgk 3-2-3 edge pairing for 5x5x5]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?34189-Durben-Virtucio-5x5-1-16.58-(2-Edges-at-a-time) Durben Virtucio 5x5 1:16.58 (2 Edges at a time)]
* Speedsolving.com: [http://www.speedsolving.com/forum/showthread.php?12727-5x5-Edges-AvG-vs.-Big-Cubes-Method 5x5 Edges; AvG vs. Big Cubes Method]
* [https://alg.cubing.net/?puzzle=6x6x6&setup=3Lw-_Lw-_3Bw-_Bw-_3Uw_Dw2_F_D2_F-_Uw2_3Uw2_Dw-_L_D2_L-_Uw-_3Uw_Dw2_B-_U-_B_Uw2_3Uw_Dw-_R_U-_R-_Uw2_3Uw_Dw_B-_D_B_Uw-_3Uw-_Dw_R-_U-_R_Uw_R_U-_R-_Uw-_3Uw-_Dw-_B_D2_B-_Dw_D_3Bw_Bw_Lw_U2_3Lw-_U2_3Lw-_U2_3Lw-_U2_3Lw-&alg=x-_U-_L-_U_Lw-_U_R2_U_Lw_U-_L_U_Lw-_U2_3Lw2_Lw-_U2_Lw_U-_R-_U2_L2_U_3Lw-_R-_U_R_U-_R2_3Lw2_U-_L-_U_3Lw-_U-_L-_U-_3Lw_U2_3Lw2_Lw_U-_L_U-_3Lw-_Lw2_U2_3Lw2_U-_L2_U-_3Lw2_Lw_U_L_U_3Lw_Lw-_U_L-_U-_3Lw2_U2_3Lw_U2_3Lw2_Lw_U2_Lw2_U2_Lw UEF8E example solve]
* [http://bbs.mf8-china.com/forum.php?mod=viewthread&tid=115522 UEF8E thread with algorithms (Chinese)]
*[https://docs.google.com/document/d/1XpvMLo9GpL7ptij2NIzce4LjPaQpai7Wu7asU_9JzPs/edit?usp=sharing 5-3 Edge Pairing Document]
[[Category:4x4x4 substeps]]
[[Category:5x5x5 substeps]]
[[Category:Big Cubes substeps]]