Puzzle: Cube, Face Cut, Type A, 4th Order, Vertex Cut, Type C, 3rd Order
Abbreviation: Cube FA4VC3
Commonly Known As: 4x4x4 + Master Skewb

Piece Counts
Name Qty Colors Orient. Perm. Orbits
Outer Corner 8 3 3 Odd None
Inner Corner 24 1 None Odd None
Outer Edge 48 1 None Even 2
Inner Edge 24 2 None Odd None
Outer Center 24 1 None Odd None
Inner Center 24 1 None Odd None

Move Types
Type Layer Period Pieces Affected Total Parity
Face 1 4 1 outer corner 4-cyc, 3 inner corner 4-cyc,
4 outer edge 4-cyc, 2 inner edge 4-cyc,
1 outer center 4-cyc, 1 inner center 4-cyc
Even
Face 2 4 2 outer edge 4-cyc, 1 inner edge 4-cyc,
2 outer center 4-cyc, 2 inner center 4-cyc
Odd
Vertex 1 3 1 outer corner twist,
1 outer corner 3-cyc, 2 inner corner 3-cyc,
6 outer edge 3-cyc, 2 inner edge 3-cyc,
4 outer center 3-cyc, 3 innter center 3-cyc
Even

Suggested Solving Orders

Reduction
1. Group inner centers
2. Group outer centers with inner centers
3. Group inner edges
4. Group subcorners with corners
5. Solve grouped pieces
6. Solve outer edges

Important Issues and Notes
The outer edges fall into two orbits which change parity together. Solving the inner edges puts the outer edge orbits in even parity.

Useful Algorithms

In step 2, three cycle outer centers: ubr+ F+ ubr- F-
In step 2, three cycle outer centers: UFR+ U+ UFR-
In step 3, three cycle inner edges: u+ R+ U+ R- u-
In step 4, three cycle subcorners: (UFR- R+ U- R- UFR+) D+ (UFR- R+ U+ R- UFR+) {D-}
In step 5, swap two reduced edges: u2 r2 U2 r2 U2 r2 u2
In step 5, parity change reduced edges: r- U2 r+ U2 r- F2 r+ F2 r- B2 r- B2 r+
In step 5, rotate one corner: (R+ UFL+ R- UFL+ R+ UFL+ R- UFL+) (F2 U+ (r+ U2 r- l- U l+) U- F2 L2 F+ (u- F2 u+ d+ F2 d-) F- L2) (L- (r+ U+ UBR- U- UBR+ U- r-) B- d+ B+ (r+ U+ UBR- U+ UBR+ U- r-) B- d- B+ L+)
In step 6, three cycle outer edges: UFR+ (R+ Bb+ D+ Bb- R-) UFR- (R+ Bb+ D- Bb- R-)