Puzzle: Cube, Face Cut, Type A, 3rd Order, Vertex Cut, Type B, 1st Order
Abbreviation: Cube FA3EB1
Commonly Known As: Nothing

Piece Counts

Name	Qty	Colors	Orient.	Perm.	Orbits
Corner	8	3	3, Fixed	Odd	None
Center	6	1	None	Odd	None
Inner Edge	24	1	None	Odd	None
Middle Edge	48	1	None	Even	2
Outer Edge	12	2	2	Odd	None

Move Types

Type	Layer	Period	Pieces Affected	Total Parity
Face	1	4	1 corner 4-cyc, 2 inner edge 4-cyc, 4 middle edge 4-cyc, 1 outer edge 4-cyc	Even
Edge	1	2	1 corner swap, 1 center swap, 1 outer edge twist, 3 inner edge swap, 8 middle edge swap, 2 outer edge swap	Even

Suggested Solving Orders

By Piece Type
1. Corners
2. Centers
3. Outer Edges
4. Inner Edges
5. Middle Edges

Important Issues and Notes
While on Cube EB1 solving the centers and corners guarantees an even flip of outer edges, it does not on this puzzle. This occurs beacuse both face and edge moves are odd permutations of corners and centers but only face moves are even flips of outer edges. A even number of total moves is required to solve the corners and centers; if an odd number of edge moves are used there will be an odd number of outer edge flips, and this can happen because face twists can make the total number of moves even.

This is a very difficult parity to deal with. The algorithm provided will flip an odd number of outer edges and keep centers and corners solves. A resolve of outer edges will be necessary. Inner edges were moved to step 4 to make this parity easier to fix.

A single swap of outer edges is not a possibility. Solving the centers requires and even number of edge twists. If there are an even number of edge twists then the parity of the outer edges becomes linked to the corner parity, just as on Cube FA3, so solved corners resolves the parity of the outer edges.

Useful Algorithms
In step 1, twist two corners: U+ UF FR UF U- FR
In step 2, three cycle centers: UR UL UR UL
In step 2, three cycle centers: (FL UL) UR (UL FL) UR
In step 2, fix parity: u+ BR BL BR BL
In step 3, three cycle outer edges: FL UR FL UR
In step 3, three cycle outer edges: r+ U2 r- U2
In step 3, swap two pair of outer edges: r2 U2 r2 U2
In step 3, flip two outer edges: DF (r+ U+ r-) DF (r+ U- r-)
In step 3, fix flip parity (resolve required): U+ FR U+ FR U+ FR U+ FR U+ FR u+ BR BL BR BL
In step 4, three cycle inner edges: (UB UL) x 3 (F+ R+ F- R-) (UL UB) x 3 (R+ F+ R- F-)
In step 4, three cycle inner edges: (UB UL) x 3 (R+ F+ R- F-) (UL UB) x 3 (F+ R+ F- R-)
In step 5, three cycle middle edges: (FL UR FL UR) (UB BR UB) (UR FL UR FL) (UB BR UB)