See: Math concepts
Come up with a meaningful definition of symmetry.
Thoughts about symmetry
Symmetry group relates:
The mind is augmented through the "symmetric group" which is the system that augments our imagination.
Symmetry group consists of distinguishable actions which accomplish nothing (leave an object invariant). So they separate the object/environment and its state.
Symmetry involves a dual point of view: for example, vertices are distinct and yet not distinguishable.