Similarities and Differences between a Rubik’s Cube and a Rhombic Dodecahedron
Cube is a cube; RD is a 12-sided puzzle with congruent rhombi as faces.
Cube has 6 centers; RD has 6 4-sided corners. Cube centers have 1 color each so orientation does not matter; RD 4-sided corners have 4 colors each and can be oriented 4 ways. Cube centers are both centers of rotation and centers of faces; RD 4-sided corners are the centers of rotation for the layers although they are not centers of the faces.
Cube has 12 edges; RD has 12 rectangular face centers. Cube edges have 2 colors each so orientation matters; RD rectangular face centers are rectangular so orientation does not matter. Cube edges are unique, so they can be double-swapped, or 3-cycled, but no single pair can be swapped; RD rectangular face centers are not unique, so can not only be double-swapped and 3-cycled, but can appear to have 2 swapped. In reality 2 of one color and 1 of another need to 3-cycle.
Cube has 8 corners; RD has 8 3-sided corners. Cube corners have 3 colors each so orientation matters; RD 3-sided corners have 3 colors each so orientation matters.
Cube has 6 colored sides; RD has 12 sides, but only 6 colors. Opposite faces are the same color.
Cube has 54 stickers; RD has 60 stickers.
Cube has 3 layers top to bottom, left to right, and front to back; so does the RD, it just isn’t as obvious since it isn’t cube-shaped.
Cube can be solved using a variety of strategies; RD can be solved using the same basic strategies as solving a cube, with the added orientation challenges mentioned above.
Strategy—Like Solving a Cube Using F2L/LL
Steps 1-5 Bottom View
Decide which 4-color corner you want to build around. This will be the center of rotation of the bottom layer.
Get 3 rectangles around it.
Using the 4th spot orient each of the 4-color corners of the middle layer.
Move said corners above their matching rectangles.
Get the 4th rectangle in the bottom layer. These first 5 steps are roughly equivalent to “get the white edges” on a normal Rubik’s Cube. That’s step 1 on a normal cube. 😀
Insert the 4 3-color corner / rectangle pairs between the solved rectangles. This is roughly equivalent to getting the F2L corner / edge pairs on a normal cube.
Orient the top 4-color corner with a simple twist of the top layer.
3-cycle the 4 top layer 3-color corners home.
Twist said corners if necessary.
3-cycle the last 4 rectangles home. Sometimes it looks like you need to swap 2. 3-cycle them along with one of the same color that is already in place.