For a physicist or a mathematician, the most symmetrical object you could think about would be a sphere, because it looks identical no matter what you do to it, however you rotate it in any given direction.

Philosophy used to be a field that had content, but then 'natural philosophy' became physics, and physics has only continued to make inroads. Every time there's a leap in physics, it encroaches on these areas that philosophers have carefully sequestered away to themselves, and so then you have this natural resentment on the part of philosophers.

Symmetries are the playing field on which the physical world works and which determine the rules of the game. The symmetries of nature determine for us things that remain constant, that can't be changed. Those are the guideposts in physics, the quantities like energy and momentum.

Lawrence M. Krauss Quotes