With an even number of plus signs, along with all the odd permutations with an odd number of plus signs, where " t"
12.
Similarly, the mirror image has either an odd permutation with an even number of plus signs or an even permutation with an odd number of plus signs.
13.
That is, is 1 if is an even permutation of, " 1 if it is an odd permutation, and 0 if any index is repeated.
14.
There are 12 ! / 2 ways to arrange the central edges, since an odd permutation of the corners implies an odd permutation of these pieces as well.
15.
There are 12 ! / 2 ways to arrange the central edges, since an odd permutation of the corners implies an odd permutation of these pieces as well.
16.
This means in 3d it is sufficient to take cyclic or anticyclic permutations of ( 1, 2, 3 ) and easily obtain all the even or odd permutations.
17.
An even permutation is one that can be represented by an even number of swaps while an odd permutation is one that can be represented by an odd number of swaps.
18.
Taking the even permutations with an odd number of plus signs, and the odd permutations with an even number of plus signs, gives a different snub cube, the mirror image.
19.
It would not be possible to swap all 15 pairs, since this would be an odd permutation of the edges, so a reducing factor of 2 14 is applied to the preceding figure.
20.
An odd permutation of the corners implies an odd permutation of the centres and vice versa; however, even and odd permutations of the centres are indistinguishable due to the identical appearance of the pieces.
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