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.