V-Cube 7

The V-Cube 7 is a 7x7x7 version of a Rubik's cube. If you already have a solid understanding of the 5x5x5 version, then the 7x7x7 should be easy enough to solve. The big difference is that there are 7 layers instead of 5. Uppercase letters will still represent faces, and lowercase represent the layers just inside of the faces (outer slices). The next layers in, adjacent to the middle, are called "inner slices" and will be denoted by a lowercase letter followed by an underscore. So going from left to right the layers on a 7x7x7 cube are:

L, l, l_, middle, r_, r, R.

This notation extends to edge and center pieces. So, UFL is the top-left corner on the front face. Moving to the right, we have UFl, UFl_, UF, URr_, UFr, and UFR.

Some pieces can be partitioned into subsets, where pieces permute within a subset but never move between subsets.

The cube contains the following pieces:

• 8 Corners (example UFR): these move just like the corners on all Rubik's Cubes.
• 60 Edges. Edges can be divided into the following sub-types:
  • 12 Middle Edges (example UF): these move like the edges on a 3x3x3 cube.
  • 48 Side Edges (example UFr or UFr_): There are two subsets, and each is isomorphic with the 24 side edges of a 5x5x5 cube or the 24 edges of a 4x4x4 cube.
• 160 Centers. Other than the Fixed Center, each subset of 24 centers includes 4 of each color, and these four are indistinguishable from one another. This simplifies the puzzle greatly since permutations of identical elements can be ignores. The centers can be divded into the following sub-types:
  • 6 Fixed Centers: these never move in relation to one another (like the 3x3x3 cube centers)
  • 48 Diagonal Centers (example uFr or u_Fr_): There are two subsets, and each is isomorphic with the 24 diagonal centers of a 4x4x4 or 5x5x5 cube.
  • 48 Middle Centers (example uF or u_F): There are two subsets and each is isomorphic with the 24 middle centers of a 5x5x5.
  • 48 Offset Centers (example uFr_ or u_Fr): There are two subsets of 24 pieces each. These pieces are unique to the 7x7x7 cube as they sit at the intersection between an inner slice, an outer slice, and a face.

The diagram below shows the arrangement of the various classes of pieces, using numbers to indicate subsets. For example a Middle Center that is adjacent to the fixed center (MC2) will always be adjacent to a fixed center and never move out to MC1.

Although the 7x7x7 has significantly more pieces than a 5x5x5 (218 versus 98), the majority of the pieces should already be familiar. Any operators that work on a 5x5x5 should have analogous operators on the 7x7x7, with the substitution of either inner or outer 7x7x7 slices for the 5x5x5's regular slices. The only new piece is the Offset Center, which winds up being one of the simpler pieces to manipulate since it is at the intersection of an inner slice, and outer slice, and a face.

Solution Outline

1. Solve the 9 centermost pieces on each face. This is identical to the start of the 5x5x5 solution, using inner slices and face moves. At the completion of this step, sets MC2 and DC2 will be solved.

1. Match the Offset Centers with their adjacent Middle Center. There will be four such groups on every face. It isn't necessary to match these to the 9 pieces solved in step 1. A modified version of the edge-3-cycle can be helpful: r_ (U' r U) r_' (U' r' U). This cycles dr_F, Ur_f, and u_rF. Note that this is the only time we're performing operators unique to the 7x7x7.

1. Now solve the entire 5x5 center just like solving the centers of a 5x5x5 cube. Use only face and outer slice moves, treating the result of step 1 as a 5x5x5 center, the results of step 2 as middle centers.

1. Match up all of the edge pieces. Once again this is like a 5x5x5 cube, although with double the work since you have two sets of side edges. The edge-3-cycle is handy here, using either inner or outer slices depending on which side edge you are fixing. If you get stuck with a 2-cycle at the end, then fix it just like you would with a 5x5x5 cube.

1. At this point you now have a 3x3x3 cube. Solve normally using only face moves.