This page describes an intutive method of solving a tetrahedron of any size. It is not a fast method of solving.
When building centers, the color of each face must be correct relative to the other faces. On some tetrahedrons, each face has a fixed center tile, so the color of each face is predetermined. Other tethrahedrons do not have a fixed center tile so the color of each face is not predetermined; any color can be created on any face. On such tetrahedrons the color of a face, relative to the other faces, is determined by the arrangement of colors on the tips of the tetrahedron.
Centers of a tetrahedron.
When building the centers, the triangular tips of the centers can be ignored because any two of them can be swapped without affecting any other centers. The center-tips do need to be solved, but can be completed last.
The black and magenta center-tips will swap positions.
Centers are created by constructing a row of color and then moving the row to another face.
The first two centers can be built by creating a row of color and then moving the row to another face. This method of building centers is faster than the alternative (shown below) and only works for building the first two centers.
For tetrahedrons that have a fixed center tile, the row containing the fixed center tile should be built first and must be built on the face containing the fixed center tile. Once the row is built, there is no need to move the row to another face.
Construct a row of color by turning the face containing the row and then adding a triangle to the row by turning a horizontal layer. When the row is complete, the row is moved to the bottom face.
Building the second center can be accomplished in a similar manner, but requires a bit more care in order to avoid damaging the first center.
One center has already been built. Construct a row of color and move it to the bottom face. Notice that each time a horizontal layer is turned, it is un-turned in order to restore the completed (blue) center.
Once two centers have been completed a different method must be used for building the last two centers. This method will work for building any center, but it is slower than the 'bar building' method described above.
This method moves a 'diamond' from one face to another face. The diamond is composed of two triangle tiles.
There is a 'left-leaning' diamond and a 'right-leaning' diamond.
Move a 'left-leaning' cyan diamond from one face to another.
Move a 'right-leaning' cyan diamond from one face to another.
In both cases above, the green diamond that is moved to the blue face can be ignored. We only need to focus on moving the cyan diamond from the blue face to the green face.
By alternating the type of diamond that is moved and by over-lapping the previous diamond that was moved, individual triangles can be placed in any order desired.
Join the cyan, magenta, and black triangles in a row.
| Step | Desc |
|---|---|
| 1-8 | Move a right-leaning diamond containing the cyan triangle. |
| 9 | Position the cyan triangle to be moved. |
| 10-17 | Move a left-leaning diamond containing the magenta triangle. |
| 18-25 | Move a right-leaning diamond containing the black triangle. |
Each diamond that was moved, over-lapped the previous diamond that was moved.
If the diamond contains a center-tip, the process of moving a left-leaning or right-leaning diamond will not work. Moving a diamond containing a center-tip is technically not necessary but can be accomplished. Center-tips can easily be swapped between any two centers; the other triangle in the diamond can be moved as part of a different diamond.
Move a diamond containing a center-tip.
Building inner-wedges on a tetrahedron is done in a similar manner as building edges on a cube.
For tetraherons with odd number of inner-wedges, start from the middle inner-wedge and build out. For tetrahedrons with an even number of inner-wedges, position and orient the edge between its two matching centers before adding an inner-wedge to the edge. This avoids building a 'backward' edge. A backward edge cannot be oriented correctly.
Inner-edge-cubies of tetrahedron.
Add the red-yellow inner-wedge to the edge.
| Step | Desc |
|---|---|
| 1 | Turn a layer to add the red-yellow inner-wedge to the edge. |
| 2 | Move the red-yellow edge out of the way |
| 3-4 | Replace the red-yellow edge with another edge |
| 5 | Un-turn the layer |
For tetrahedrons with an even number of inner-wedges on an edge, ensure that the edge matches the two centers before adding an inner-wedge.
Add the red-yellow inner-wedge to the edge. The edge has an even number of inner-wedges.
| Step | Desc |
|---|---|
| 1 | Turn a layer to add the red-yellow inner-wedge to the edge. |
| 2 | Move the red-yellow edge out of the way |
| 3-4 | Replace the red-yellow edge with another edge |
| 5 | Un-turn the layer |
For tetrahedrons with an odd number of inner-wedges on an edge, start with the central inner-wedge and build outwards. In the example below, the edge matches the two centers, but this is only done for clarity. For tetrahedrons with an odd number of inner-wedges on an edge, the edge does not need to match the two centers.
Add the red-yellow inner-wedge to the edge. The edge has an odd number of inner-wedges.
| Step | Desc |
|---|---|
| 1 | Join red-yellow |
| 2 | Move red-yellow out of the way |
| 3-4 | Replace red-yellow with new edge. |
| 5 | Un-turn face |
| 6-7 | (Optional) Return the red-yellow edge. |
Inner-wedges can be added to the edges one-at-a-time, but just like solving edges on a cube, the last three inner-wedges must be strategically positioned so that they are all solved at the same time.
Move the corners to their home positions. The orientation of the corners is not important and can be ignored.
(Optional) Twist all tips so that the color matches their neighbor.
Move all corners to their home positions. The orientation of the corners can be ignored. This example uses the green face, but any color face can be used.
| Step | Desc |
|---|---|
| 1 | Turn a face so that all three green corners are in the layer with the green center. |
| 2 | Turn the green layer clockwise or anti-clockwise which will move all corners to their home positions. |
(Optional) Twist all corners to match the centers.
Twisting the corners to match the centers verifies that all corners are in their home positions. This is only a temporary measure because the next stage of the solve will change the orientations of the corners.
Use Hs2 to move edges to their home positions.
When moving edges to their home positions, their orientation can be ignored because any un-oriented edges will be corrected in the next stage of the solve. However, when moving edges to their home positions, you may wish to also ensure that the edges are oriented correctly because orienting the edges while positioning them takes less work than positioning all edges first and then orienting all the edges.
Hs2 cycles edges clockwise. The purple tip is only for reference and can be ignored.
| Step | Desc |
|---|---|
| 1-4 | HedgeSlammer |
| 5-8 | HedgeSlammer |
When Hs2 is applied, all corners are returned to their home positions, but will change orientation.
The example below shows one technique for moving edges to their home positions. For clarity, the entire edge is colored. When solving a real tetrahedron only the inner-wedges will be solved. The outer-wedges will not be solved.
Position (and optionally orient) one edge.
Pre-stage the cyan and red edges so that when Hs2 is applied they will both be moved to their correct position (and optionally oriented) in the bottom layer.
| Step | Desc |
|---|---|
| 1-8 | Hs2 |
Use Hs2 to position (and optionally orient) the final three edges.
Use Hs2 to correctly orient the edges.
In order to orient the edges, you must understand how Hs2 affects the edges.
In the examples below, the outer wedges have been colored for clarity. When solving a real tetrahedron, only the inner wedges will be solved; the outer wedges wil not be solved.
After applying Hs2, the blue-green edge has 'rotated' counter-clockwise around the green center, the blue-red edge has 'rotated' counter-clockwise around the blue center, and the green-red edge has 'flipped' over the red center.
| Step | Desc |
|---|---|
| 1-8 | Hs2 |
Applying Hs2 three times is the same as doing nothing because all tiles are returned to their starting position and orientation. However, if a 'pivot' is added, then two edges will be flipped. The pivot is covered in much more detail in the solution to the cube.
Adding a pivot to (Hs2)3 flips the green-red edge and flips the blue-red edge.
| Step | Desc |
|---|---|
| 1-8 | Hs2 |
| 9-16 | Hs2 |
| Pivot | |
| 17-24 | Hs2 |
| Un-pivot | |
By flipping two edges at a time, all un-oriented edges can be oriented correctly.
Twist the corners to orient them so they match the centers. If necessary, twist the tips so that they match their neighbors.
Twist the corners (and tips) to match the centers.
The centers, inner-edges, corners, and tips are solved.
Outer-wedges of tetrahedron.
The outer-wedges can be moved to their home positions and oriented correctly by using 'FaceSlammer'. The FaceSlammer is a modified form of a HedgeSlammer. Similar turns are performed, but they are performed on a face, rather than along an edge.
FaceSlammer cycles three outer-wedges counter-clockwise and flips two of them.
| Step | Desc |
|---|---|
| 1-4 | FaceSlammer |
If FaceSlammer is applied three times, it is the same as doing nothing.
| Step | Desc |
|---|---|
| 1-4 | FaceSlammer |
| 5-8 | FaceSlammer |
| 9-12 | FaceSlammer |
Another example of FaceSlammer. FaceSlammer cycles three outer-wedges counter-clockwise and flips two of them.
| Step | Desc |
|---|---|
| 1-4 | FaceSlammer |
In theory, all outer-wedges can be moved to their home positions and oriented correctly using nothing but FaceSlammers, but doing so in practice can be quite difficult. It is much easier to solve the outer-wedges by turning and un-turning a face.
Turning (and un-turning) a face makes solving outer-wedges easier.
| Step | Desc |
|---|---|
| 1 | Turn face prior to FaceSlammer (Setup) |
| 2-5 | FaceSlammer |
| 6 | Un-turn face (Teardown) |
Any face can be turned (and un-turned) to help solve an outer-wedge.
If desired, multiple faces can be turned prior to applying FaceSlammer. Any faces that are turned prior to applying FaceSlammer must be un-turned in the reverse order after applying FaceSlammer.
Applying FaceSlammer affects three outer-wedges, but it is not necessary to solve all three at once. Outer-wedges can be solved one-at-a-time until three unsolved outer-wedges remain. The last three unsolved outer-wedges must be solved together. It is almost always necessary to temporarily un-solve some outer-wedges in order to maneuver the final three unsolved outer-wedges into a position where they can be solved.