1. Any permutation of the corners is possible, including odd permutations . 2. Any permutation of the wedge pieces is possible, including even and odd permutations . 3. Any permutation of the corners is possible, including odd permutations , giving 8 ! possible arrangements. 4. Any permutation of the outer edges is possible, including odd permutations , giving 24 ! arrangements. 5. In terms of permutations the two group elements of are the set of even permutations and the set of odd permutations . 6. In three dimensions only, the cyclic permutations of are all even permutations, similarly the anticyclic permutations are all odd permutations . 7. Any permutation of the edges is possible, including odd permutations , giving 24 ! arrangements, independently of the corners or centres. 8. Taking the odd permutations of the above coordinates with an even number of plus signs gives another form, the enantiomorph of the other one. 9. An odd permutation followed by an odd permutation will represent an overall even permutation ( adding two odd numbers always returns an even number ). 10. An odd permutation followed by an odd permutation will represent an overall even permutation ( adding two odd numbers always returns an even number ).
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