Puzzle: Octahedron, Face Cut, Type A, 3rd Order
Abbreviation: Octa FA3
Commonly Known As: Nothing

Piece Counts

Name	Qty	Colors	Orient.	Perm.	Orbits
Corner	6	4	2, Fixed	Even	None
Edge	12	2	None	Even	None
Face	24	1	None	Even	2

Move Types

Type	Layer	Period	Pieces Affected	Total Parity
Face	1	3	1 corner 3-cyc, 1 edge 3-cyc, 3 face 3-cyc	Even
Face	2	3	2 edge 3-cyc, 2 face 3-cyc	Even

Suggested Solving Orders

By Piece Type
1. Solve edges, use corner as starting reference
2. Place corners, orient some if possible
3. Orient corners
4. Solve faces

Important Issues and Notes
Due to identical pieces, an apparent single swap of faces is possible. This is solved with a simple 3 cycle including two faces of the same color.

At this level it begins to become apparent that these octahedra only ever have 4 colors on any specific face. In fact, 4 of the faces contain all of 4 colors of stickers, and the other 4 faces contain the other stickers. This can be empirically shown by scrambling a high-order puzzle.

Useful Algorithms
In step 2, three cycle corners (DFN): (R+ U+ R-) D+ (R+ U- R-) D-
In step 3, twist two corners (DFN): (R+ U+ R- U- R+ U+ R-) D+ (R+ U- R- U+ R+ U- R-) D-
In step 4, three cycle centers (UFN): (F+ u+ F-) D+ (F+ u- F-) D-