Summary: Symmetry is all pervasive -- from the day/night cycle to the rise and fall of the tides, from geometry to physics. It is thus natural that mathematicians should want to study symmetry, to quantify it, to exploit it. At its core, this article is about quantifying the amount of symmetry in an object and separating those that, in a certain well-defined sense, possess a large amount of symmetry from those that possess only a small amount.