Hoya method
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The Hoya Method is a 4x4 speedsolving method proposed by JongHo Jeong. It can also be applied to bigger cubes, and is frequently done on both 5x5x5 (usually under the name Hoya5) and 4x4x4. It's a submethod of Reduction.
Contents
Beginner Overview
 Solve 2 opposite centers. (Must NOT be your cross color)
 Solve D center (cross color) and one other adjacent center.
 Solve the 4 dedges of the cross using the last 2 unsolved centers; placed on U and F. (cross edges step)
 Solve the last 2 centers(L2C).
 Solve the last 8 dedges(L8E).
 Solve as a 3x3x3 + Parities if encountered.
Normal Overview
 Solve any 2 centers; opposite or adjacent. [Note: If solving opposite centers, solve as in 'Beginner Overview' above. If adjacent centers, continue below.]
 Solve last 2 adjacent centers while ensuring cross color is placed on D before next step. (cross color center must be included in either step 1 or 2)
 Solve the 4 dedges of the cross using the last two unsolved centers; placed on U and F. (cross edges step)
 Solve the last 2 centers(L2C).
 Solve the last 8 dedges(L8E).
 Solve as a 3x3x3 + Parities if encountered.
Pros
 Easy last 8 dedge pairing.
 Cross is completed prior to 3x3x3 stage.
Cons
 Slightly higher movecount compared to Yau. Although, the movecount is close.
Notable users
 JongHo Jeong
 Luke Tycksen
 Dylan Clark
 Aaron LoPrete
 Chris Brotzman
 Alaik Bhatia