Puzzle: Cube, Face Cut, 4th Order
Abbreviation: Cube FA4
Commonly Known As: Rubik's Revenge, Master Cube, 4x4x4

Piece Counts

Name	Qty	Colors	Orient.	Perm.	Orbits
Corner	8	3	3, Fixed	Odd	None
Edge	24	2	None	Odd	None
Center	24	1	None	Odd	None

Move Types

Type	Layer	Period	Pieces Affected	Total Parity
Face	1	4	1 corner 4-cyc, 2 edge 4-cyc, 1 center 4-cyc	Even
Face	2	4	1 edge 4-cyc, 2 center 4-cyc	Odd

Suggested Solving Orders

Reduction
1. Solve centers, use corners to detemine position
2. Group edges
3. Solve as Cube FA3, fix parities as encountered

Cage
1. Group edges
2. Solve corners and edges
3. Fix parity if necessary
4. Solve centers

Important Issues and Notes
The reduction steps are quite quick, easy, and convenient, however the huge downfall to this method is that the parity is nearly impossible to detect until midway through the final solve. By contrast, the parity can be detected a good bit earlier in the cage method. Either way, it is a difficult parity to fix.

Useful Algorithms
In reduction step 2, three cycle edges: u+ R+ U+ R- u-
In reduction step 3, parity change edges: r- U2 r+ U2 r- F2 r+ F2 r- B2 r- B2 r+
In reduction step 3, swap two reduced edges: u2 r2 U2 r2 U2 r2 u2