Puzzle: Cube, Face Cut, Type A, 3rd Order
Abbreviation: Cube FA3
Commonly Known As: Rubik's Cube, Magic Cube, 3x3x3

Piece Counts

Name	Qty	Colors	Orient.	Perm.	Orbits
Corner	8	3	3, Fixed	Odd	None
Edge	12	2	2, Fixed	Odd	None
Center	6	1	None	None	None

Move Types

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

Suggested Solving Orders

Block Building Heise-Like
1. Build a 2x2x2 block
2. Expand to two 2x2x3 blocks
3. Solve edges
4. Place corners
5. Orient corners

Important Issues and Notes
The layer 2 face turn is a bit odd. The centers cannot permute relative to each other, so a "center 4-cycle" is a bit meaningless. However, those 4 centers do move relative to the rest of the puzzle. Also this makes sense since the move must be an even permutation because it is equivalent to two layer 1 turns in the other direction.

This is the most studied and practiced twisty puzzle in the world, plenty of much more detailed solutions exist elsewhere.

Useful Algorithms
In step 4, three cycle corners: (R+ U+ R-) D+ (R+ U- R-) D-
In step 5, twist two corners: (R+ U+ R- U- R+ U+ R-) D+ (R+ U- R- U+ R+ U- R-) D-