* Rubik 3x3x4 *

* Made by Cube 4 You (C4U), 2009. *

(plastic, 2.2 by 2.2 by 3 inches;
white body has opposite sides white / blue, red / orange, green / yellow,
the same as the color scheme as the standard Rubik's 3x3x3;
black body has opposite sides black / white, red / yellow, green / blue)

This extension of the standard
*Rubik 3x3x3*
cube allows only 180 degree rotations in two of the dimensions.
One solution approach is to think of an "outer"
*Rubik 2x2x3 Domino*
formed by the top and bottom layers with an "inner" domino in the middle:

1.
Solve the outer domino.

2.
Solve the inner domino,
except if your solution makes use of flips of the front, back, or left sides,
replace each such flip by a flip of the right side
(that is,
rotate the middle layers appropriately,
flip the right side, rotate the middle layers back).

3. If Step 2 ended up using an even number of flips,
then the puzzle is solved.
Otherwise,
perform the following transformation, adapted from
*Jaap's Page*
for the domino,
that does nothing to the middle two layers
(by exchanging an upper and lower middle edge)
using an odd number of flips:
** D2 R M- (D2 R) **^{3} M R D2

**Notation:**
R denotes a flip of the right face,
M a 90 degree clockwise rotation of the middle two layers
(with respect to looking down from the top),
D and D- clockwise and counter clockwise rotations of the lower middle layer
(with respect to looking up from the bottom),
2 and 3 mean do it two or three times.

**Further Reading**

*Jaap's Page*,
from: http://www.jaapsch.net/puzzles/cube334.htm
(Presents a similar approach with many additional transformations.)