A Rubik's family cube has the properties detailed in the Cube definitions topic. It is a three-dimensional component with six square faces of equal size. The standard Rubik's cube has three rows of three facelets (square visible coloured surfaces or stickers) on each of the cube's six faces. In the context of the Unravel program the standard Rubik's cube is referred to as a size 3 cube. The Unravel program provides the means for solving cubes within the size range 2 to MaxCubeSize which has a program upper limit of size 99 reachable for most monitors but such a large size, or large sizes in general, may be too difficult for many users to handle.
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A size 4 cube is illustrated on the left. |
For a size n cube there will be (n x n x 6) facelets. The overall cube comprises a number of sub-cube elements. These are referred to as corner cubies, edge cubies and centre cubies. When referring to these sub-cube elements the corner, edge or centre qualifier will always be used in this on-line help. For standard style cubes the centre cubies are unmarked (same colour cubies appear identical). A style variant which uses marked centre cubies is available as an option for the Unravel program for cubes up to about size 32 when Numerical marking is in use and up to about size 99 when the Corner marking extension applies.
Corner cubies have three facelets, edge cubies have two facelets and centre cubies have only one facelet. The total number of cubies nc in a size n cube is given by:
nc = 6 (n - 2)2 + 12 (n - 2) + 8
The following table provides numerical values for cubes in the size range 2 to 16.
Size |
No. of |
No. of 12 (n - 2) |
No. of |
Total |
No. of |
2 | 8 | 0 | 0 | 8 | 24 |
3 | 8 | 12 | 6 | 26 | 54 |
4 | 8 | 24 | 24 | 56 | 96 |
5 | 8 | 36 | 54 | 98 | 150 |
6 | 8 | 48 | 96 | 152 | 216 |
7 | 8 | 60 | 150 | 218 | 294 |
8 | 8 | 72 | 216 | 296 | 384 |
9 | 8 | 84 | 294 | 386 | 486 |
10 | 8 | 96 | 384 | 488 | 600 |
11 | 8 | 108 | 486 | 602 | 726 |
12 | 8 | 120 | 600 | 728 | 864 |
13 | 8 | 132 | 726 | 866 | 1014 |
14 | 8 | 144 | 864 | 1016 | 1176 |
15 | 8 | 156 | 1014 | 1178 | 1350 |
16 | 8 | 168 | 1176 | 1352 | 1536 |
For cubes of any size, the number of corner cubies remains the same. The number of edge cubies rises as a linear function of cube size. The number of centre cubies rises as a function of the size of the cube squared. For standard cubes with unmarked centres that may imply a preference for aligning centre cubies sooner rather than later. The same preference may apply for centre cubies in all but the final layer for marked cubes. Alignment of centre cubies in the final layer is likely to be best left to last when all other alignment actions have been completed.