Similarities and Differences between a Rubik’s Cube and an Octahedral 3x3x3
- Cube is a cube; Octahedral is an 8-sided puzzle with equilateral triangles as faces.
- Cube has 6 centers; Octahedral has 6 corners. Cube centers have 1 color each so orientation does not matter; Octahedral corners have 4 colors each and can be oriented 4 ways. Cube centers are both centers of rotation and centers of faces; Octahedral 4-sided corners are the centers of rotation for the layers although they are not centers of the faces.
- Cube has 12 edges; Octahedral has 12 edges. Cube edges and Octahedral edges both have 2 colors each so orientation matters; Cube edges and Octahedral edges are both unique, so they can be double-swapped, or 3-cycled, but no single pair can be swapped.
- Cube has 8 corners; Octahedral has 8 centers. Cube corners have 3 colors each so orientation matters; Octahedral centers have 1 color each so orientation matters not.
- Cube has 6 colored sides; Octahedral has 8 colored sides.
- Cube has 54 stickers; Octahedral has 56 stickers.
- Cube has 3 layers top to bottom, left to right, and front to back; so does the Octahedral, it just isn’t as obvious since it isn’t cube-shaped.
- Cube can be solved using a variety of strategies; Octahedral 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 the Ultimate Solution
- Pick a corner to be the base. The base is the middle of the bottom layer.
- Twist the bottom layer so that the 4 corners in the middle layer are in the correct places relative to the bottom corner.
- Twist the middle layer corners so the colors line up correctly relative to the bottom corner and each other.
- Use simple moves to insert the 4 bottom layer edges.
- Use simple moves to insert 3 of the middle layer edges. Note: in steps 4 and 5 make sure you end up with the corners still oriented correctly after each edge is inserted.
- Twist the top so the top corner is solved.
- Insert the 2 top layer edges that are farthest from the unsolved edge in the middle layer. (Make sure you keep the top corner solved while doing so.)
- This leaves 3 edges to solve. Use the EPS of the Ultimate Solution.
- Use the CPS of the Ultimate Solution to get all the centers into place. In other words, use a commutator to 3-cycle the centers into place.
Strategy—Like Solving a Cube Using F2L/LL
- Decide which 4-color corner you want to build around. This will be the center of rotation of the bottom layer.
- Get the 4 adjacent edges and the corners on the other ends of these edges. Orient the corners as you go.
- Insert the 4 center / edge pairs between the solved edges and middle layer corners.
- Orient the top corner with a simple twist of the top layer.
- 3-cycle the 4 top layer edges home. It may take two 3-cycles.
- Twist said edges if necessary.
- 3-cycle the last 4 centers home. It may take two 3-cycles.