Visualizing Automorphisms of S6
The Weird Symmetry of Shuffling Six Items Visualizing the Exceptional Automorphism of S 6 When shuffling around items, there's something strangely unique about shuffling precisely six items. In fact, it's so weird, that mathematicians refer to it as "exceptional" or "exotic". This is an interactive post exploring this exceptional property, and trying to visualize just what the heck is going on. We're going to build up to the following diagram, along with the concepts needed to understand it.