Editing Rubik's Cube (section)

===Centre faces===
The original Rubik's Cube had no orientation markings on the centre faces (although some carried the "Rubik's Cube" mark on the centre square of the white face), and therefore solving it does not require any attention to orienting those faces correctly. However, with marker pens, one could, for example, mark the central squares of an unscrambled Cube with four coloured marks on each edge, each corresponding to the colour of the adjacent face; a cube marked in this way is referred to as a "supercube". Some Cubes have also been produced commercially with markings on all of the squares, such as the [[Lo Shu Square|Lo Shu]] [[magic square]] or [[playing card]] [[suit (cards)|suits]]. Cubes have also been produced where the nine stickers on a face are used to make a single larger picture, and centre orientation matters on these as well. Thus one can nominally solve a Cube yet have the markings on the centres rotated; it then becomes an additional test to solve the centres as well.

Marking Rubik's Cube's centres increases its difficulty, because this expands the set of distinguishable possible configurations. There are 4<sup>6</sup>/2 (2,048) ways to orient the centres since an even permutation of the corners implies an even number of quarter turns of centres as well. In particular, when the Cube is unscrambled apart from the orientations of the central squares, there will always be an even number of centre squares requiring a quarter turn. Thus orientations of centres increases the total number of possible Cube permutations from 43,252,003,274,489,856,000 (4.3×10<sup>19</sup>) to 88,580,102,706,155,225,088,000 (8.9×10<sup>22</sup>).<ref>{{cite journal
 | last = Hofstadter | first = Douglas R. | author-link = Douglas Hofstadter
 | date = March 1981
 | issue = 3
 | journal = [[Scientific American]]
 | jstor = 24964321
 | pages = 20–39
 | title = Metamagical themas: The Magic Cube's cubies are twiddled by cubists and solved by cubemeisters
 | volume = 244| doi = 10.1038/scientificamerican0381-20 }}; see p. 22</ref>

When turning a cube over is considered to be a change in permutation then we must also count arrangements of the centre faces. Nominally there are 6! ways to arrange the six centre faces of the cube, but only 24 of these are achievable without disassembly of the cube. When the orientations of centres are also counted, as above, this increases the total number of possible Cube permutations from 88,580,102,706,155,225,088,000 (8.9×10<sup>22</sup>) to 2,125,922,464,947,725,402,112,000 (2.1×10<sup>24</sup>).