7x7x7 Rubik's Cube

The 7x7x7 Rubik's Cube is also known as the "V-Cube 7" in other designs. The first mass-produced 7×7×7 Rubik's Cube was invented by Panagiotis Verdes and was produced by the Greek company Verdes Innovations SA. Other such puzzles have since been introduced by a number of Chinese companies, some of which have mechanisms which improve on the original. Like the 5×5×5, the V-Cube 7 has both fixed and movable center facets.

About the Rubik's Cube
The puzzle consists of 284 unique miniature cubes ("cubies") on the surface. Six of these (the central tiles of the six faces) are attached directly to the internal "spider" frame and are fixed in position relative to one another. Each piece (or quintet of edge pieces) shows a unique color combination, but not all combinations are present (for example, there is no piece with both red and orange sides, since red and orange are on opposite sides of the solved Rubik's Cube). The location of these cubes relative to one another can be altered by twisting the outer layers of the Cube 90°, 180° or 270°, but the location of the colored sides relative to one another in the completed state of the puzzle cannot be altered: it is fixed by the relative positions of the fixed center squares and the distribution of color combinations on edge and corner pieces. Currently, the V-Cube 7 is produced with white plastic as a base, with red opposite orange, blue opposite green, and yellow opposite black. The fixed black center piece is branded with the letter "V". Verdes also sells a version with black plastic and a white face, with the other colors remaining the same, solid plastic versions with the plastic the color itself and no stickers, flag variations of the 7x7x7 Rubik's Cube including Germany, Poland, Russia etc. The V-Cube 7 is noticeably rounded. This departure from a true cube shape is necessary, since the mechanism used on this puzzle would not function properly with layers of identical thickness. Other means (such as magnets) would be required. The rounded shape of the V-Cube 7 results in corner stickers that are similar in size to the center stickers, which helps hide the unequal thickness. The Rubik's Cubes from other manufacturers can be found with rounded or flat sides, but all use thicker outer layers.

Facts
The 7x7x7 Rubik's Cube has 6 fixed centers, 210 other center pieces, 60 edge pieces, and 8 corners.

There are 19,500,551,183,731,307,835,329,126,754,019,748,794,904,992,692,043,434,567,152,132,912,323,232,706,135,469,180,065,278,712,755,853,360,682,328,551,719,137,311,299,993,600,000,000,000,000,000,000,000,000,000,000,000, about 1.95×10160, or about 232 duoquinquagintillion possible combinations.

However, a fixed center piece is marked with a V, which can be oriented four different ways. This increases the number of patterns by a factor of four to 7.80×10160, although any orientation of this piece could be regarded as correct.

The fastest time to solve a 7x7x7 Rubik's Cube is 2 minutes and 18.13 seconds and was achieved by Feliks Zemdegs at the Cubing Classic Event on 18–19 March 2017 in Melbourne, Australia.

Notation
Let the faces be denoted by the letters L, R, F, B, U and D (Left, Right Front, Back, Up and Down). Clockwise quarter turns of a face layer are denoted by the appropriate letter, anti-clockwise quarter turns by the letter with an apostrophe (i.e. L', R', F', B', U' or D'). Half turns are denoted by the letter followed by a 2 (i.e. L2, R2, F2, B2, U2 or D2). The above is the same notation as for the 3×3×3 cube. An internal slice will be denoted by adding a subscript 2, 3 or 4. So F2 is a clockwise turn of the slice immediately behind the Front face, and F3' is an anti-clockwise turn of the slice immediately behind that. Note that these denote a slice only, so such a move will not disturb the corners of the cube. The location of any piece can be denoted by listing the three faces/slices it lies in.

How To Solve
2. Match Up the Inner Edges - In this phase the inner edge pieces are matched up to form matching pairs. 3. Match Up the Outer Edges - In this phase the outer edge pieces are matched up to the middle/inner edge triplets. 4. Solve the Cube. More information on how to solve the 7x7x7 Rubik's cube here.
 * 1) Solve Centers - The method below solves the U centers without disturbing any already solved faces. Simply repeat this for each of the faces.
 * 2) Find any center piece edge that belongs on the U face. Hold the cube so that it lies on the F or face.
 * 3) If the piece is in the front face, turn F to put the piece at the top right, i.e. in the U2 or U3 layer, and the R2, R3, or R4 slice. If it is in the bottom face, turn D to put the piece at the front right, i.e. in the F2 or F3slice, and the R2, R3, or R4 slice.
 * 4) Turn the U face so that there is an incorrect piece at the back right location where the piece belongs.
 * 5) Do one of the following move sequences to insert the center piece:  1. From F U2 R4 to U B2 R4: Do R4 U' L2' U R4' U' L2  2. From F U2 R3 to U B2 R3: Do R3 U' L2' U R3' U' L2  3. From F U2 R2 to U B2 R2: Do R2 U' L2' U R2' U' L2  4. From F U3 R4 to U B3 R4: Do R4 U' L3' U R4' U' L3  5. From F U3 R3 to U B3 R3: Do R3 U' L3' U R3' U' L3  6. From F U3 R2 to U B3 R2: Do R2 U' L3' U R2' U' L3  7. From D F2 R4 to U B2 R4: Do R42 U' L22 U R42 U' L22  8. From D F2 R3 to U B2 R3: Do R32 U' L22 U R32 U' L22  9. From D F2 R2 to U B2 R2: Do R22 U' L22 U R22 U' L22  10. From D F3 R4 to U B3 R4: Do R42 U' L32 U R42 U' L32  11. From D F3 R3 to U B3 R3: Do R32 U' L32 U R32 U' L32  12. From D F3 R2 to U B3 R2: Do R22 U' L32 U R22 U' L32
 * 6) Repeat steps 1-4 until all 24 center pieces in the U face are correct.
 * 7) Repeat steps 1-5 for each of the faces.
 * 1) Find any inner edge piece that is not yet matched up with its middle edge piece. Hold the cube so that this piece lies at the U F R3 location.
 * 2) Find the matching middle edge piece. Use any face moves to bring it to the U B location.
 * 3) Check that the middle edge piece shows a different color on the U face than the inner edge piece. If not, then flip over the middle edge piece by doing B' U R' U'.
 * 4) Find any unmatched inner edge piece and put it at the U R B3 location, without disturbing the other two pieces. If there is no other unmatched inner edge, then do U2 R3 U2 R3 U2 R3 U2 R3U2 R3 to make some new unmatched inner edge pairs and try again.
 * 5) Do R3 B'RB R3'.
 * 6) Repeat steps 1-4 until all inner edges are matched up with the middle edges.
 * 1) Find any outer edge that is not yet matched up with its middle triplet. Hold the cube so that this piece lies at the U F R2 location.
 * 2) Find the matching edge triplet. Use any face moves to bring them to the U B location.
 * 3) Check that the triplet shows a different color on the U face than the outer edge piece. If not, then flip over the triplet by doing B' U R' U'.
 * 4) Find any other unmatched outer edge piece and put it at the U R B2 location without disturbing the other pieces. If there is no other unmatched pair, then do U2 R2 U2 R2 U2 R2 U2 R2 U2 R2to make some new unmatched outer edges and try again.
 * 5) Do R2 B'RB R2'.
 * 6) Repeat steps 1-5 until all edges lie in matching edge quintuplets.
 * 1) Solve the cube by turning outer faces only, using any method for the 3×3×3 cube.