This puzzle is a cube which is built from smaller cubes, 7 to an edge, i.e.
a 7×7×7 cube. Like a Rubik's Cube each slice can rotate, which
rearranges the small cubes on the surface of the puzzle. The six sides of
the cube are coloured, so every corner piece shows three colours, every edge
piece shows 2 colours, and every face centre only one.
The VCubes worldwide patent was granted to inventor Panagiotis Verdes on
2 December 2004, WO 2004 103497.
The number of positions:
There are 8 corner pieces with 3 orientations each, 12 middle edge pieces with 2 orientations
each, 24 inner edge pieces and 24 outer edge pieces apparently with 2 orientations each. There
are 6 types of centre pieces, 24 pieces of each type. This gives a maximum of
8!·12!·24!
^{8}·3
^{8}·2
^{60}
positions. This limit is not reached because:
 The total twist of the corners is fixed (3)
 The total flip of the middle edges is fixed (2)
 The permutation of the corners and middle edges is even (2)
 The inner/outer edge orientation is dependent on its position, i.e. inner and outer edges cannot actually be flipped (2^{48})
 There are indistinguishable face centres (4!^{6·6})
This leaves 8!·12!·24!^{8}·3^{7}·2^{10} / 4!^{36} =
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
= 1.95·10^{160} positions.
Like the normal cube, there are several types of solution. Here I will only give
the 'EdgeMatching' solution method.
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, anticlockwise 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 F_{2} is a clockwise
turn of the slice immediately behind the Front face, and F_{3}' is an
anticlockwise 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.
Solution
Phase 1: Solve centres
The method below solves the U centres without disturbing any already solved
faces. Simply repeat this for each of the faces.
 Find any centre piece edge that belongs on the U face. Hold the cube so that it
lies on the F or D face.
 If the piece is in the front face, turn F to put the piece at the
top right, i.e. in the U_{2} or U_{3} layer, and the R_{2},
R_{3}, or R_{4} slice. If it is in the bottom face, turn D to put the piece at the
front right, i.e. in the F_{2} or F_{3} slice, and the R_{2},
R_{3}, or R_{4} slice.
 Turn the U face so that there is an incorrect piece at the back right location where
the piece belongs.

Do one of the following move sequences to insert the centre piece:
1. From F U_{2} R_{4} to U B_{2} R_{4}: Do R_{4} U' L_{2}' U R_{4}' U' L_{2}
2. From F U_{2} R_{3} to U B_{2} R_{3}: Do R_{3} U' L_{2}' U R_{3}' U' L_{2}
3. From F U_{2} R_{2} to U B_{2} R_{2}: Do R_{2} U' L_{2}' U R_{2}' U' L_{2}
4. From F U_{3} R_{4} to U B_{3} R_{4}: Do R_{4} U' L_{3}' U R_{4}' U' L_{3}
5. From F U_{3} R_{3} to U B_{3} R_{3}: Do R_{3} U' L_{3}' U R_{3}' U' L_{3}
6. From F U_{3} R_{2} to U B_{3} R_{2}: Do R_{2} U' L_{3}' U R_{2}' U' L_{3}
7. From D F_{2} R_{4} to U B_{2} R_{4}: Do R_{4}2 U' L_{2}2 U R_{4}2 U' L_{2}2
8. From D F_{2} R_{3} to U B_{2} R_{3}: Do R_{3}2 U' L_{2}2 U R_{3}2 U' L_{2}2
9. From D F_{2} R_{2} to U B_{2} R_{2}: Do R_{2}2 U' L_{2}2 U R_{2}2 U' L_{2}2
10. From D F_{3} R_{4} to U B_{3} R_{4}: Do R_{4}2 U' L_{3}2 U R_{4}2 U' L_{3}2
11. From D F_{3} R_{3} to U B_{3} R_{3}: Do R_{3}2 U' L_{3}2 U R_{3}2 U' L_{3}2
12. From D F_{3} R_{2} to U B_{3} R_{2}: Do R_{2}2 U' L_{3}2 U R_{2}2 U' L_{3}2
 Repeat ad until all 24 centre pieces in the U face are correct.
 Repeat ae for each of the faces.
Phase 2: Match up the inner edges.
In this phase the inner edge pieces are matched up to form matching pairs.
 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 R_{3} location.
 Find the matching middle edge piece. Use any face moves to bring it to the U B location.
 Check that the middle edge piece shows a different colour on the U face than the inner edge piece.
If not, then flip over the middle edge piece by doing B' U R' U'.
 Find any unmatched inner edge piece and put it at the U R B_{3} location, without
disturbing the other two pieces. If there is no other unmatched inner edge, then do U2 R_{3} U2
R_{3} U2 R_{3} U2 R_{3} U2 R_{3} to make some new unmatched inner
edge pairs and try again.
 Do R_{3} B'RB R_{3}'.
 Repeat ad until all inner edges are matched up with the middle edges.
Phase 3: Match up the outer edges.
In this phase the outer edge pieces are matched up to the middle/inner edge triplets.
 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 R_{2} location.
 Find the matching edge triplet. Use any face moves to bring them to the U B location.
 Check that the triplet shows a different colour on the U face than the outer edge piece.
If not, then flip over the triplet by doing B' U R' U'.
 Find any other unmatched outer edge piece and put it at the U R B_{2} location
without disturbing the other pieces. If there is no other unmatched pair, then do
U2 R_{2} U2 R_{2} U2 R_{2} U2 R_{2} U2 R_{2}
to make some new unmatched outer edges and try again.
 Do R_{2} B'RB R_{2}'
 Repeat ae until all edges lie in matching edge quintuplets.
Phase 4: Solve the cube.
 Solve the cube by turning outer faces only, using any method for the 3×3×3 cube. This is always possible.