Solve a hexahedron twisty puzzle (cube) of any size

This page describes an intutive method of solving a hexahedron (cube) of any size. It is not a fast method of solving.

• Build centers
• Swap centers
• Build edges
• Solve cube
• Correct parity

Build centers

When building centers, the color of each face must be correct relative to the other faces. On odd-cubes, each face has a fixed center-cubie, so the color of each face is predetermined. Even-cubes 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 cubes the color of a face, relative to the other faces, is determined by the arrangement of colors on the corner-cubies.

Centers are created by building rows of color and then collecting the rows on another face.

Completed rows are collected on another face.

Once four centers have been completed a different method must be used for building the last two centers. The following method will work for building any center, but it is slower than the 'row building' method described above.

Tiles on diagonals can easily be replaced with tiles from other faces.

Tiles which are not on a diagonal are more difficult to replace.

Centers are built in 'rings' that start in the middle and expand outward. Each ring is composed of four bars. The bars grow longer as the ring expands.

To create a ring, each bar of the ring must be created. To create a bar, each tile of the bar must be added to the bar. A bar is created by adding one tile at a time.

Anytime a bar needs to be created, it can be created by adding one tile at a time until the bar has been built. The process will eventually create a bar, but it is a slow process. A bar can be built faster by adding multiple tiles at once.

In the example below, adding two tiles completes the bar. When solving a real cube, completing a bar (especially a long one) may not be so simple and may require several iterations of adding tiles.

The example below illustrates creating an outer ring. (Although not shown, all inner rings should have already been created.) The ring is created by building four bars. For the sake of clarity, the creation of each bar has been extremely simplified.

Once the fourth bar has been created, the ring has been created.

Odd-cubes are completed in a similar manner, but the diagonals and rings are slightly different. In the examples below, the magenta center tile is only for reference and can be ignored.

Swap centers

Swapping centers should not normally be needed, but can fix centers that were created on the wrong face.

On odd-cubes, the center tile of each face determines the color of the face. On even-cubes, the face colors can be determined by examining corner-cubies.

Swapping centers in this way preserves all edges.

Build edges

The example below illustrates completing an edge that is already built. Scrambled cubes do not have edges that are already built. The edges must be built by joining matching edge-cubies in pairs, then in triplets, etc.

The green-white edge has been completed, but the red centers (and other edges) have been broken. They need to be fixed.

Edge-cubies can be added to edges one-at-a-time, however, the last three unsolved edge-cubies must be stategically positioned so that all three edges are solved simultaneously.

The same three edges that are shown above are rearranged below, but are solved in the same manner.

When completing the final three edges, the orientation of the last three un-solved edge-cubies can be ignored. As long as the edge-cubies are joined to their matching edges, the edge-cubies will be automatically oriented correctly.

Building edges may sometimes result in having exactly two remaining edge-cubies on two different edges that must be swapped. To solve this, unsolve the two edges along with another edge and then re-solve the three 'broken' edges simultaneously.

Solve cube

After the edges have been built, the cube can be solved in the same manner as solving a 3x3x3 however, in even-cubes a parity issue may occur.

Correct parity

A parity issue can arise in even-cubes larger than a 2x2x2. A parity issue occurs when there is a mismatch between the number times that edge-cubies and corner-cubies have been turned. The cube cannot be solved until the parity issue has been corrected.

Correcting parity is very easy. Re-solving the cube after parity has been corrected takes a little bit of work.

Odd-cubes can also have a parity-like issue, but the issue can be entirely avoided if edges are built by starting from the middle edge-cubie and building outwards.

To fix parity on even-cubes, turn any inner slice, one quarter turn. Doing so will disrupt some completed centers and edges.

Fixing the parity issue is easy, but the issue can be re-introduced just as easily. Fortunanely, if the move-sequences in this guide are followed, the parity issue will not be re-introduced. (As long as the inner layers are turned an even number of times, the parity issue will not reoccur.)

Since the centers and edges were disrupted they must be rebuilt.

Once the centers have been rebuilt, the edges must be rebuilt.

After the edges have been rebuilt, the cube can be solved in the same manner as solving a 3x3x3.