This page describes an intutive method of solving a face-turning octahedron of any size. It is not a fast method of solving.
An octahedron has eight faces, but they do not all interact. The eight faces are split into two groups of four faces. The tiles on the faces of each group can be scrambled together, but the tiles can never be scrambled with tiles in the other group.
Only four faces interact. The tiles on gray faces will never land on a colored face and tiles on colored faces will never land on a gray face.
A hedgeSlammer. The turning faces intersect along an edge.
Applying HedgeSlammer 60 times (which requires 240 quarter-turns) is the same as doing nothing.
Corner pieces on an octahedron do not 'twist', instead, they 'flip' between two different orientations. Any reference to twisting corners should be interpreted to mean 'flipping'.
Building centers is conceptually similar to building centers on a tetrahedron.
Centers
Center-tips can easily be swapped with center-tips on another face in the group.
Replace a magenta center-tip with the black center-tip.
Left-leaning and right-leaning diamonds can be replaced.
Move a 'left-leaning' magenta diamond from one face to another.
Move a 'right-leaning' magenta diamond from one face to another.
In both cases above, the blue diamond that is moved to the light-blue face can be ignored. We only need to focus on moving the magenta diamond from the light-blue face to the blue face.
Move three corners to their home positions. This can be done by simply turning faces. The three corners must not all be on the same face. The corners do not need to be oriented correctly but understanding the state of the cube is much easier if they are.
For octahedrons that have centers, ensure the corners are positioned on the correct face.
Position three corners in a 'line'.
Ensure centers are correct.
The remaining three corners can be moved to their correct positions by using HedgeSlammer.
Cycle three (cyan, magenta, black) corners using HedgeSlammer.
| Step | Desc |
|---|---|
| 1-4 | Apply HedgeSlammer then spin 180 degrees |
| 5-8 | Apply HedgeSlammer then spin 180 degrees |
Once the corners have been positioned, they must be oriented correctly.
Twist two adjacent corners. The magenta and black corners will be twisted.
| Step | Desc |
|---|---|
| 1-4 | HedgeSlammer |
| Spin 180 degrees | |
| 5-12 | Hs2 |
| Spin 180 degrees | |
| 13-16 | HedgeSlammer |
Twist two opposite corners. The magenta and black corners will be twisted.
| Step | Desc |
|---|---|
| 1-8 | Apply Hs2 then spin 180 degrees |
| 9-16 | Apply Hs2 then spin 180 degrees |
Since applying a HedgeSlammer always twists four corners, either method above can be used to correctly orient corners, regardless of whether the twisted corners are adjacent to each other or opposite each other.
If you try to twist two adjacent corners using the method which twists two opposite corners, it will result in an octahedron with two opposite corners that are twisted.
Similarly, if you try to twist two opposite corners using the method which twists two adjacent corners, it will result in an octahedron with two adjacent corners that are twisted.
Solve all corner tiles of the octahedron.
Corner tiles of an octahedron.
The following method will will work on any size octahedron, but it is not intuitive. The method cycles three corner-tiles without affecting any other tiles.
The cyan, magenta, and block corner tiles will cycle clockwise.
| Step | Desc |
|---|---|
| 1-4 | Modified HedgeSlammer |
| 5-8 | Modified HedgeSlammer |
| 9-12 | Modified HedgeSlammer |
| 13-16 | Modified HedgeSlammer |
| 17-20 | Modified HedgeSlammer |
On all octahedrons larger than a 3x3, applying a single Modified HedgeSlammer will cycle the cyan, magenta, and black corner tiles anti-clockwise.
The following method is an intuitive method of solving the corner-tiles, but only works on octahedrons larger than a 3x3.
Divide the octahedron into a top and bottom. The horizontal blue face is the top face. The horizontal orange face on bottom. with the magenta triangles pointing up and the cyan triangles pointing down.
Any of the corner tiles on the top face can be moved to any of the three side faces that touch it points.
Move the corner tile on the top face to the top corner on the purple face.
Move the corner tile on the top face to the lower-left corner on the purple face.
Move the corner tile on the top face to the lower-right corner on the purple face.
If the corner tiles on the side faces are not solved, but all the corner tiles on top face have been solved, move one of the unsolved corner tiles from a side face to the top face.
Once the corner tiles on all three side faces has been completed, the corner tiles on the top face will have automatically been completed.
Flip the cube over making the orange face the top face. Repeat the process of moving the corner-tiles from the top face to their home positions on the three side faces.
Inner-wedges of a octahedron.
Even-octahedrons (e.g. 4x4, 6x6) have a central inner-wedges. The central inner-wedges must be solved before the other inner-wedges are solved. Odd-octahedrons (e.g. 5x5, 7x7) do not have central inner-wedges.
The inner-wedges can be moved to their home positions by using 'FaceSlammer'. The FaceSlammer is a modified form of HedgeSlammer. Similar turns are performed, but they are performed on a face, rather than along an edge.
Applying FaceSlammer six times is the same as doing nothing.
| Step | Desc |
|---|---|
| 1-4 | FaceSlammer |
| 5-8 | FaceSlammer |
| 6-12 | FaceSlammer |
| 13-16 | FaceSlammer |
| 17-20 | FaceSlammer |
| 21-24 | FaceSlammer |
By strategically turning a face, three central inner-wedges can be cycled.
Replace the magenta central inner-wedge with the black central inner-wedge. The cyan inner-wedge can be ignored.
| Step | Desc |
|---|---|
| 1 | Turn face |
| 2-5 | FaceSlammer |
| 6 | Un-turn face |
| 7-10 | FaceSlammer |
| 11-14 | FaceSlammer |
| 15-18 | FaceSlammer |
| 19-22 | FaceSlammer |
| 23-26 | FaceSlammer |
A shortened process can be used on octahedrons that are larger than 4x4.
| Step | Desc |
|---|---|
| 1 | Turn face |
| 2-5 | FaceSlammer |
| 6 | Un-turn face |
| 7-10 | FaceSlammer |
| 11-14 | FaceSlammer |
All central inner-wedges (if they exist) should be in their home positions before solving other inner-wedges.
Two examples of how to replace an inner-wedge are given below.
Replace the magenta inner-wedge with the black inner-wedge. The cyan inner-wedge can be ignored.
Replace the magenta inner-wedge with the black inner-wedge. The cyan inner-wedge can be ignored.
Outer wedges of an octahedron.
Odd-octahedrons (e.g. 5x5, 7x7) have central outer-wedges. The central outer-wedges must be solved before the other outer-wedges are solved. Even-octahedrons (e.g. 4x4, 6x6) do not have central outer-wedges.
The outer-wedges can be moved to their home positions by using 'FaceSlammer'. The FaceSlammer is a modified form of HedgeSlammer. Similar turns are performed, but they are performed on a face, rather than along an edge.
Applying a FaceSlammer alters six outer-wedges.
| Step | Desc |
|---|---|
| 1-4 | FaceSlammer |
Applying FaceSlammer three times is the same as doing nothing.
| Step | Desc |
|---|---|
| 1-4 | FaceSlammer |
| 5-8 | FaceSlammer |
| 9-12 | FaceSlammer |
By strategically turning a face, three central outer-wedges can be cycled.
Cycle three central outer-wedges clockwise.
| Step | Desc |
|---|---|
| 1 | Turn face |
| 2-5 | FaceSlammer |
| 6 | Un-turn face |
| 7-10 | FaceSlammer |
| 11-14 | FaceSlammer |
All central outer-wedges (if they exist) should be in their home positions before solving other outer-wedges.
Two examples of how to replace an outer-wedge are given below.
Replace the magenta outer-wedge with the black outer-wedge. The cyan outer-wedge can be ignored.
Replace the magenta outer-wedge with the black outer-wedge. The cyan outer-wedge can be ignored.
If needed, a face can be turned prior to replacing an outer-wedge. The face must be un-turned after the outer-edge has been replaced.