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These 8 permutations form one of the 3 Dih4 subgroups of S4

The 8 permutations of a square, which form the hyperoctahedral group of dimension 2, i.e. the dihedral group Dih4

These are passive permutations, i.e. the permutations are denoted by the result of applying them. The orientation of the permutation matrix fits prefix notation.



These 8 permutations applied on a 2-ary Boolean function generate all the functions in its bec, and the 4 permutations on the left generate all the functions in the sec

Compare 3-ary Boolean functions; cube permutations, the 3-dimensional equivalent.
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Date/TimeThumbnailDimensionsUserComment
current20:49, 9 August 2019Thumbnail for version as of 20:49, 9 August 2019822 × 909 (987 KB)Watchduckmake odd permutations dark
17:41, 26 November 2016Thumbnail for version as of 17:41, 26 November 2016822 × 909 (593 KB)Watchduckdetails
23:11, 7 October 2016Thumbnail for version as of 23:11, 7 October 2016822 × 909 (652 KB)Watchduck{{Information |Description ={{en|1=The 8 permutations of a square, which form the hyperoctahedral group of dimension 2, i.e. the dihedral group [[w:Examples_of_groups#dihedral_group_of_order_8|Dih<sub...

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