Rubik's 2x3x3 Domino

Designed by Erno Rubik 1983; left purchased circa 1985; right purchased 2009.
(plastic, 1.5 inches high by 2.25 inches square)

Put the numbers in order on both sides.

Notation: R for a flip of the right side, U, D for clockwise rotations of the up and down faces (- for counterclockwise, and 2 to do it twice). We also use M to denote rotating the whole puzzle 90 degrees clockwise (with respect to looking down), as a convenience so that only right flips are needed (easier to hold and also useful for the solution to Rubik 3x3x4).

Move pieces to their correct layers:

1. Repeatedly position pairs of edges on the wrong layers on the right and do R.

2. Repeatedly position two corners on the wrong layers at the front right and do:
Exchange UFR and DFR:   R   U   R   U-   R
Solve the two layers independently:

3. Use this to permute corners; X = Step 2 transformation, Y = reverse of X:
Exchange URF and URB:   X   M-   Y   D-
4. Use this to permute edges:
Exchange UF and UR:   (R   U)2   (R   U2)2   X
Jaap's Page presents the transformations above (and others), as well as the following transformation to change a side to its mirror image (F denotes a front flip):
R F T- F T2 R (T F)2 T2 R T- F R
Further reading:
Jaap's Page, from:
McFarren's Page, from: