Talk:Full octahedral group

dictionary of permutations and their properties

At the end of this page, there is a nice Pastebin link to a dictionary of permutations and their properties. I assume that 'letters' refers to the positions of the axes. For example, 'A', 'C','B' would mean that the x-axis is on the position of the x-axis, y is on the position of z and z at the position of y. When writing some code, I noticed that the 'letters' for group (0,3) to (7,3) and (0,4) to (7,4) are switched. That means, that the 'letters' for (0,3) to (7,3) should be CAB instead of BCA and (0,4) to (7,4) should have the 'letters' BCA instead of CAB. @Watchduck is this a mistake or am I missing something? Wnukx (discuss • contribs) 09:50, 21 December 2023 (UTC)

permutation (3, 2) with signed letters (¬A, ¬C, B)

@Wnukx: The negators and letters in this dictionary describe the signed letters you see in the SVG images. They correspond to the rows of the 3×3 signed permutation matrix to their left (and also of the 3×8 binary matrix to their right). For many purposes you probably want to describe the columns of the 3×3 matrix instead. Greetings, Watchduck (quack) 11:18, 4 January 2024 (UTC)